Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-8 Complex Numbers - Practice and Problem-Solving Exercises - Page 253: 15

Answer

$|2-2i|=2\sqrt{2}$

Work Step by Step

The plot of the given complex number, $ 2-2i ,$ is shown below. The absolute value of the complex number $a+bi,$ written as $|a+bi|,$ is given by $\sqrt{a^2+b^2}.$ Therefore, the absolute value of the given complex number is \begin{align*} & \sqrt{(2)^2+(-2)^2} \\&= \sqrt{4+4} \\&= \sqrt{8} \\&= \sqrt{4\cdot2} \\&= 2\sqrt{2} .\end{align*} Hence, $ |2-2i|=2\sqrt{2} .$
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