## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 769: 94

#### Answer

The absolute value of a complex number $a+ib$ is the shortest length from the origin to the point $a+ib$. To determine the absolute value of $a+ib$, apply the Pythagorean Theorem or distance formula from the origin $\left( 0,0 \right)$ to the point $a+ib$ $\left( a,b \right)$.

#### Work Step by Step

Let $z=a+ib$, then the absolute value of point $z$ is represented by $\left| z \right|$ $\left| z \right|=\sqrt{{{a}^{2}}+{{b}^{2}}}$ Example: The above explanation can be justified with the help of an example. Let $z=4+i3$ be a complex number, then the absolute value of $z$ is, \begin{align} & \left| z \right|=\sqrt{{{4}^{2}}+{{3}^{2}}} \\ & =\sqrt{25} \\ & =5 \end{align} In this example $5$ is the absolute value of the complex number $z=4+i3$

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