Absolute Value. The absolute value (or modulus) of a real number is the corresponding nonnegative value that disregards the sign. For a real value, a, the absolute value is: a, if a is greater than or equal to zero. -a, if a is less than zero. abs(-0) returns 0. For example, the absolute value of 4 is 4 : − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 4. This seems kind of obvious. Of course the distance from 0 to 4 is 4 . Where absolute value gets interesting is with negative numbers. For example, the absolute value of − 4 is also 4 : − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 4. Take out all the face cards and jokers and divide the deck between two people. 1) Each player lays down one card at a time. 2) Find the absolute value of each card. The player with the highest absolute value wins that round and takes both cards. 3) Continue until all cards have been played. So if we want to sort it from least to greatest, well, we just have to start at the left end of the number line. The smallest of them, or the least of them, is -28. Then we go to -17. -17. Then we go to 22.4. Then we go to 22.4. And then we go to the absolute …The complex number is, We know that, The absolute value of a complex number x + iy, is defined as the distance between the origin (0, 0) and the point (x, y) in the complex plane. Its value is calculated by, Now, by using the above formula the absolute value of the complex number is, ⇒ =. To learn more about absolute value visit:\[\therefore \]The absolute value of \[4 + 3i\] is 5. Note: Many students make the mistake of writing both the values i.e. \[ + 5\] and \[ - 5\] in the final answer which is wrong as the absolute value or modulus is always positive as it denotes the distance between the complex number and the origin.a. Solve for x: 4 x - 1 + 7 ≤ 14. We can simplify this inequality by subtracting 7 from each side, so let's start with that: 4 x - 1 ≤ 7. After that, we need to split the inequality into two separate ones since we're working with absolute value. The two inequalities will be: 4 x - 1 ≤ 7 and 4 x - 1 ≥ -7.The absolute maximum and minimum value of f (x)= 3x4 −8x3 +12x2 −48x+25,x ∈ [0,3] are respectively. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:the absolute value of 4xx4 if 0 x 4 is.Absolute Value. The absolute value (or modulus) of a real number is the corresponding nonnegative value that disregards the sign. For a real value, a, the absolute value is: a, if a is greater than or equal to zero. -a, if a is less than zero. abs(-0) returns 0. We would like to show you a description here but the site won’t allow us. Testing solutions to absolute value inequalities. In this math lesson, we learn how to determine if given values of x satisfy various absolute value inequalities. We examine three different inequalities and test each x value to see if it meets the inequality's conditions.An absolute value inequality is an inequality that contains an absolute value expression. For example, ∣ x < 2 and ∣ ∣ x ∣ > 2 are absolute value inequalities. Recall that x 2 means the distance between ∣ ∣ x and 0 is 2. The inequality x ∣ ∣ > 2 means the distance between x and 0 is greater than 2. than 2.a. Solve for x: 4 x - 1 + 7 ≤ 14. We can simplify this inequality by subtracting 7 from each side, so let's start with that: 4 x - 1 ≤ 7. After that, we need to split the inequality into two separate ones since we're working with absolute value. The two inequalities will be: 4 x - 1 ≤ 7 and 4 x - 1 ≥ -7.The general form of absolute value notation equation is: F (x) = k + a |x - h|. This equation used by the absolute value graph calculator, where, k and h tell about how the graph shifts vertically and horizontally. The variable "a" tells us how far the value graph stretches vertically, and whether the graph opens down or up.More Examples. Here are some more examples of how to handle absolute values: |−3×6| = 18. Because −3 × 6 = −18, and |−18| = 18. −|5−2| = −3. Because 5−2 = 3 and then the …The absolute value of a number is the distance between that number and zero. For instance, the absolute value of 7 is 7, the absolute value of -5 is 5, and the absolute value of 0 is 0 ...Calculating the derivative of absolute value is challenging at first, but once you learn the formula, you can easily find the right values and functions in any problem. You will need to use many terms when working with derivatives, including continuity, discontinuity, piecewise, limits, and differential. Quick Navigation.Here's how to calculate the mean absolute deviation. Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points. Following these steps in the example below is ...The absolute value of a number a a, denoted |a| | a |, is the distance from a to 0 on the number line. Absolute value answers the question of "how far," and not "which way." The phrase "how far" implies "length" and length is always a nonnegative quantity. Thus, the absolute value of a number is a nonnegative number. Sample Set A.If the number is not negative then the absolute value of the number is itself. Thus the absolute value of 6 is 6, the absolute value of 1/3 is 1/3 and the absolute value of 0 is 0. If the number is negative then to find the absolute value you just drop the negative sign. Thus the absolute value of -2 is 2 and the absolute value of -1/7 is 1/7 ...2sqrt13 "the absolute value of a complex number is" •color(white)(x)|x+yi|=sqrt(x^2+y^2) "here "x=-6" and "y=4 rArr|-6+4i| =sqrt((-6)^2+4^2) =sqrt52=sqrt4xxsqrt13 ...Define absolute value. absolute value synonyms, absolute value pronunciation, absolute value translation, English dictionary definition of absolute value. n. 1. The numerical value of a real number without regard to its sign. For example, the absolute value of -4 is 4. Also called numerical value .About absolute value equations. Solve an absolute value equation using the following steps: Get the absolve value expression by itself. Set up two equations and solve them separately.Equations : Tiger Algebra gives you not only the answers, but also the complete step by step method for solving your equations |2x-4|=8 so that you understand betterExplore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.Simplify the expression. three tenths squared minus 17 plus the quantity negative 7 divided by the absolute value of 4.3 minus 7.8 end quantity times 2.67 This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.The absolute value is denoted as |x| or abs (x), and functions such that: |x| = x. and. |-x| = x. For example, the numbers 2 and -2 have a distance of 2 from 0, so their absolute …absolute value: 1 n a real number regardless of its sign Synonyms: numerical value Types: modulus the absolute value of a complex number Type of: definite quantity a specific measure of amountExplore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.From what I've found, it's $\sqrt {(2^2 + 3^2 + 4^2)}$ for the absolute value. ... Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.Calculating the derivative of absolute value is challenging at first, but once you learn the formula, you can easily find the right values and functions in any problem. You will need to use many terms when working with derivatives, including continuity, discontinuity, piecewise, limits, and differential. Quick Navigation.Absolute Value. In the opening activity, you saw that a difference needs to be calculated in different ways depending on whether the first value is greater or less than the second value. This problem can be solved using absolute value. This concept is often explored by imagining distance above and below zero by comparing it to sea level. The distance of a number from zero (sea level) can be ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Mean absolute deviation describes the average distance between the values in a data set and the mean of the set. For example, a data set with a mean average deviation of 3.2 has values that are on average 3.2 units away from the mean. A group of kids in town A has a bake sale every week for 5 weeks, making $40, $40, $50, $55, and $65. Their mean sales are ... Free absolute value equation calculator - solve absolute value equations with all the steps. Type in any equation to get the solution, steps and graph. This lesson is about graphing an absolute value function when the expression inside the absolute value symbol is linear. It is linear if the variable “[latex]x[/latex]” has a power of [latex]1[/latex]. The graph of absolute value function has a shape of “V” or inverted “V”. Absolute Value Function in Equation Form.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.In order to "undo" the absolute value signs, we could either get a positive or negative value, since the absolute value of \( - 5 \) is the same as the absolute value of \( 5 \), which is \( 5 \). This becomes a method where we have multiple cases. The main steps (for dealing with linear/multiple linear absolute value inequalities) areAlternatively, NumPy's np.abs() can convert list elements to their absolute values.. NumPy: Convert array elements to absolute values (np.abs, np.fabs) Difference between math.fabs() and abs(). math.fabs() also returns the absolute value but always as a floating point number (float), unlike abs().Even for integers (int), math.fabs() returns a floating point number (float).Shift absolute value graphs Get 3 of 4 questions to level up! Scale & reflect absolute value graphs Get 3 of 4 questions to level up! Graph absolute value functions Get 3 of 4 questions to level up! Quiz 1. Level up on the above skills and collect up to 240 Mastery points Start quiz. Piecewise functions.Solution. Here's the ideal situation to apply our new concept of distance. Instead of saying "the absolute value of x minus 3 is 8," we pronounce the equation |x − 3| = 8 as "the distance between x and 3 is 8.". Draw a number line and locate the number 3 on the line. Recall that the "distance between x and 3 is 8.".We can see two scale factors applied to n(x): 3 on the output value and 1/4 for the input value. Applying what we know on vertical and horizontal stretches, we have n(x) = 3·m(1/4 · x). Meaning, n(x) is the result of m(x) being vertically stretched by a scale factor of 3 and horizontally stretched by a scale factor of 1/4.The absolute maximum and minimum value of f (x)= 3x4 −8x3 +12x2 −48x+25,x ∈ [0,3] are respectively. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:the absolute value of 4xx4 if 0 x 4 is.Includes lessons Absolute Value Solution Sets, Absolute Value Inequalities with One Variable, and Absolute Value Inequalitiea with Two Variables. If we plot the real numbers on the real number line, the absolute value of any real number is simply its distance from 0 on the real number line. Similarly, we plot the complex numbers on the complex plane. In the complex plane, the origin represents the number 0. Thus, the absolute value of a complex number is the distance between that number ... Hence the absolute value of complex number. z = 46 - 4i is √2132. Question 4: Find the absolute value of the following complex number. z = 3 - 5i. Solution: The absolute value of a real number is the number itself and represented by modulus, To find the absolute value of complex number, Given : z = 3 - 5i. We have : |z| = √(a 2 +b 2)The absolute value is denoted as |x| or abs (x), and functions such that: |x| = x. and. |-x| = x. For example, the numbers 2 and -2 have a distance of 2 from 0, so their absolute …From what I've found, it's $\sqrt {(2^2 + 3^2 + 4^2)}$ for the absolute value. ... Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.The absolute value of complex number is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex number's absolute value is measured on the complex number plane.The absolute value of the slope of the demand curve D1 is, and the absolute value of the slope of demand curve D2 is 16 D1 12t- 10 4 D2 2t o 2 4 6 8 10 12 14 16 18 20 Quantity 。12:2 2112 。5/4; 4/5 0 4/55/4 . Show transcribed image text. There's just one step to solve this.Find step-by-step Algebra 2 solutions and your answer to the following textbook question: Find the absolute value of 4 - 3i..A low absolute neutrophil count is referred to as neutropenia . This occurs when the ANC is less than 2,500 cells/mcL. At levels below 1,000, you are at an increased risk of infection. A high absolute neutrophil count is called neutrophilia . This occurs when the ANC is over 6,000 cells/mcL.The absolute value of a real number x is the distance between this number and zero. We denote it by |x|. Algebraically: |x| = x if x is non-negative; and. |x| = -x if x is …Integrating an Absolute Value Z 4 0 jx3 5x2 + 6xjdx There is no anti-derivative for an absolute value; however, we know it's de nition. jxj= ˆ x if x 0 x elsewise Thus we can split up our integral depending on where x3 5x2 + 6x is non-negative. x3 5x2 + 6x 0: x(x2 5x+ 6) 0: x(x 2)(x 3) 0:The absolute value of a number measures its distance to the origin on the real number line. Since 5 is at 5 units distance from the origin 0, the absolute value of 5 is 5, |5|=5. Since -5 is also at a distance of 5 units from the origin, the absolute value of -5 is 5, |-5|=5: We are ready for our first inequality. Find the set of solutions for.Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system. This can apply to scalar or vector quantities. The symbol for absolute value is a pair of vertical lines, one on either side of the quantity whose absolute value is to be determined.This paper designs a 4-bit absolute value detector using CMOS logic and Pass-Transistor Logic (PTL). It can compare the input binary number with the set threshold, which can detect the peak signal to reduce the interference of noise and improve the detection accuracy of the signal.Includes lessons Absolute Value Solution Sets, Absolute Value Inequalities with One Variable, and Absolute Value Inequalitiea with Two Variables.The absolute value of a complex number, a + ib (also called the modulus ) is defined as the distance between the origin (0, 0) and the point (a, b) in the complex plane. To find the absolute value of a complex number, we have to take square root of the sum of squares of real and part imaginary part respectively. |a + ib| = √ (a2 + b2) Unit 10: Absolute value & piecewise functions. Piecewise functions piece together different functions. Absolute value graphs make a V shape, but why do they do that? Let's explore how to make some new and interesting types of graphs. Definition: Absolute Value. Absolute value for linear equations in one variable is given by. If |x| = a, then x = a or x = −a If | x | = a, then x = a or x = − a. where a a is a real number. When we have an equation with absolute value, it is important to first isolate the absolute value, then remove the absolute value by applying the ...The absolute value of a number corresponds to its magnitude, without considering its sign, if it has it. Geometrically, it corresponds to the distance of a point x x to the origin 0 0, on the real line. Mathematically the absolute value of a number x x is represented as |x| ∣x∣ . Due to the geometric nature of its interpretation, the ... Now that we can graph an absolute value function, we will learn how to solve an absolute value equation. To solve an equation such as 8 = | 2 x − 6 |, 8 = | 2 x − 6 |, we notice that the absolute value will be equal to 8 if the quantity inside the absolute value is 8 or -8. This leads to two different equations we can solve independently. An ndarray containing the absolute value of each element in x. For complex input, a + ib , the absolute value is \(\sqrt{ a^2 + b^2 }\) . This is a scalar if x is a scalar.fabs () function of math.h header file in C programming is used to get the absolute value of a floating point number. This function returns the absolute value in double. Syntax: double fabs (double a); Parameter: It will take a single parameter which is to be converted to an absolute value. Return Value: While passing values to fabs (), we …The number doctors look at is called your absolute neutrophil count (ANC). For a healthy person, the normal range for an ANC is between 2,500 and 6,000. The ANC is found by multiplying the WBC count by the percent of neutrophils in the blood. For instance, if the WBC count is 8,000 and 50% of the WBCs are neutrophils, the ANC is 4,000 (8,000 × ...Theorem: Extreme valUE theorem. Assume z = f (x,y) z = f ( x, y) is a differentiable function of two variables defined on a closed, bounded set D D. Then f f will attain the absolute maximum value and the absolute minimum value, which are, respectively, the largest and smallest values found among the following: The values of f f at the critical ...The general form of an absolute value function is f (x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions. General form of an absolute value equation: f ( x) = a | x − h | + k. The variable a tells us how far the graph stretches vertically, and whether the graph opens up or ... its distance from zero on the number line. * For the notation, we use two big vertical lines. Check it out: Find the absolute value of 4: Find the absolute value of -5: continue. 1. of 2. This prealgebra lesson defines and explains how to find the absolute value of a number. Facts about Absolute Value 4: absolute value in mathematics. Absolute value is one of the important topics in mathematics. You can also find it in other mathematical settings. The ordered rings, quaternions, complex numbers, and vector spaces are defined using absolute value. Absolute Value Learning.51 The absolute value of a number represents the distance from the graph of the number to zero on a number line. 52 A definition that changes depending on the value of the variable. This page titled 1.1: Review of Real Numbers and Absolute Value is shared under a CC BY-NC-SA 3.0 license and was authored, ...Simplify the expression. three tenths squared minus 17 plus the quantity negative 7 divided by the absolute value of 4.3 minus 7.8 end quantity times 2.67 This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.pandas.Series.abs. #. Return a Series/DataFrame with absolute numeric value of each element. This function only applies to elements that are all numeric. Series/DataFrame containing the absolute value of each element. Calculate the absolute value element-wise. For complex inputs, 1.2 + 1j, the absolute value is a 2 + b 2.Recall that in its basic form f (x) = |x|, f ( x) = | x |, the absolute value function is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign.In other words it is the magnitude or size of a number, no negatives allowed. The symbol "|" is placed either side to mean "Absolute Value", so we write: |−6| = 6. Try it yourself: Absolute Value. Illustrated definition of Absolute Value: How far a number is from zero. Examples: 6 is 6 away from zero, so the absolute value of 6 is 6 minus6...Here's how to calculate the mean absolute deviation. Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points. Following these steps in the example below is ...The absolute value of a number is its distance from zero on a number line . For instance, 4 and − 4 have the same absolute value ( 4 ). So, the absolute value of a positive number is just the number itself, and the absolute value of a negative number is its opposite. The absolute value of 0 is 0 . Easy!What is Absolute Difference? Absolute difference is the size of the difference between any two numbers. You can think of this as the distance between the two numbers on a number line. Whether the numbers are positive or negative, absolute difference tells you the value of this distance. Examples of Absolute Difference Formula Calculations: 1.Algebra Properties of Real Numbers Additive Inverses and Absolute Values. 2 Answers Wataru Nov 11, 2014 Remember that the absolute value sign is a negative sign eraser, so we have: #{(|-10|=10),(|10|=10):}# I hope that this was helpful. Answer link. Firelight Nov 11 ...Returns a value of the same type that is passed to it specifying the absolute value of a number. Syntax. Abs(number) The required number argument can be any valid numeric expression. If number contains Null, Null is returned; if it is an uninitialized variable, zero is returned. Remarks. The absolute value of a number is its unsigned magnitude.The absolute value of a number is the magnitude of that number regardless of the sign before it. For example, the absolute value of both -4 and 4 is 4. Let's look at the left side of the equation, -abs(-4).The absolute value of a number is its distance from 0. The absolute value of a number is the magnitude of that number without considering its sign. Since 0 is zero units away from itself, the absolute value of 0 is just 0. The absolute value of 0 is written as |0| and is equal to 0. Thus, the absolute value of 0 = |0| = 0.Absolute Operator @ Besides the ABS() function, you can use the absolute operator @: @ expression. In this syntax, the @ operator returns the absolute value of the expression. Examples. The following example shows how to use the ABS() function to calculate the absolute value of a number: SELECT ABS (-10.25) result; Code language: CSS (css) The ...
5.4. Absolute values and the triangle inequality. The triangle inequality is a very simple inequality that turns out to be extremely useful. It relates the absolute value of the sum of numbers to the absolute values of those numbers. So before we state it, we should formalise the absolute value function.. Game lion game
$\begingroup$ "To do it analytically, get rid of the absolute value: x^2−4≥0 if and only if −2≤x≤2" Shouldn't the inequality for this part be <0 or am I missing something? $\endgroup$ - Oofy2000. Mar 9, 2023 at 23:28Absolute. Menu Path : Operator > Math > Arithmetic > Absolute The Absolute Operator calculates the absolute value of the input. For example, an input value of (4 ,0, -4) outputs (4, 0, 4). This Operator accepts input values of various types. For the list of types this Operator can use, see Available Types.. Operator propertiesStep 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result! The solve for x calculator allows you to enter your problem and solve the equation to see the result. So the absolute value of negative 1 is 1. And the absolute value of 1 is also 1 away from 0. It's also equal to 1. So on some level, absolute value is the distance from 0. But another, I guess simpler way to think of it, it always results in the positive version of the number. The absolute value of negative 7,346 is equal to 7,346. Question 764709: Find the absolute value of the complex number 4 + 4i Find the absolute value of the complex number -3 - 6i Find the absolute value of the complex number 5 - 4i. Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website! Rule: |a+bi| = sqrt[a^2+b^2]How To: Given an absolute value equation, solve it. Isolate the absolute value expression on one side of the equal sign. If c > 0 c > 0, write and solve two equations: ax+b = c a x + b = c and ax+b =−c a x + b = − c. In the next video, we show examples of solving a simple absolute value equation.When you find the absolute deviation you find the mean of a data set. 1+4+5+7+8=25. 25 divided by 5 is 5. That is the mean. Then, we get multiple number out of it, which is the step I don't really get. (I was trying to solve a problem with 47, 45, 44, 41, and 48. When you add them up, you get 225, and divide it by 5.The absolute value of a number is its distance from 0. The absolute value of a number is the magnitude of that number without considering its sign. Since 0 is zero units away from itself, the absolute value of 0 is just 0. The absolute value of 0 is written as |0| and is equal to 0. Thus, the absolute value of 0 = |0| = 0.One of the most common applications of absolute value, aside from simply calculating absolute value of numbers is its use on equations. For example. |x - 1 | = 3 ∣x−1∣ =3. corresponds to a absolute value equation, because there is an equation that needs to be solved for x x, and there is an absolute value involved in there.Returns a value of the same type that is passed to it specifying the absolute value of a number. Syntax. Abs(number) The required number argument can be any valid numeric expression. If number contains Null, Null is returned; if it is an uninitialized variable, zero is returned. Remarks. The absolute value of a number is its unsigned magnitude.Definitions: The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line. Furthermore, the absolute value ...Q2. Find the absolute value of a number -3/4. Q3. Find the absolute value of complex number 4 + 9i. Q4. Find the absolute value of complex number 3 - 2i. FAQs on Absolute Value What is Absolute Value in Algebra? The absolute value of a number is defined as a numeric value regardless of the sign of the number.Simply enter two real numbers in the input sections and hit the calculate button to avail the Absolute Difference of two numbers in a matter of seconds. 4. Why is the Absolute Value of a number always positive? Absolute Value is always positive as it is the distance of a number from zero in the number line.This lesson is about graphing an absolute value function when the expression inside the absolute value symbol is linear. It is linear if the variable "[latex]x[/latex]" has a power of [latex]1[/latex]. The graph of absolute value function has a shape of "V" or inverted "V". Absolute Value Function in Equation Form.8 years ago. Well, the simple answer is that the absolute value of a number simply is the positive form of the number. |98| = 98. |-17362| = 17362. |-pi| = pi. That's the easiest way. Just get rid of the negative sign and boom, you've done the absolute value. But that's not really the point.Example 4: Solve the absolute value equation [latex]\left| { - 2x + 7} \right| = 25[/latex] . You may think that this problem is complex because of the [latex]-2[/latex] next to the variable [latex]x[/latex]. However, that shouldn't intimidate you because the key idea remains the same. We have the absolute value symbol isolated on one ... Now that we can graph an absolute value function, we will learn how to solve an absolute value equation. To solve an equation such as 8 = | 2 x − 6 |, 8 = | 2 x − 6 |, we notice that the absolute value will be equal to 8 if the quantity inside the absolute value is 8 or -8. This leads to two different equations we can solve independently. Lesson. The absolute value of a number is its distance from zero (0) on a number line. This action ignores the "+" or "-" sign of a number because distance in mathematics is never negative. You identify an absolute value of a number by writing the number between two vertical bars referred to as absolute value brackets: |number|.He calculated the absolute value of z, |z|, where you square the real parts of z, and then add them and take the square root. So, if z = a + bi. then the real parts are a and b. In this case z = √ (3)/2 + i. Then a = √ (3)/2. and b = 1, because the real part of i is 1, just as the real part of 2i is 2. The absolute value of z is:.