# Chapter 4 Quadratic Functions and Factoring - 4.6 Perform Operations with Complex Numbers - 4.6 Exercises - Skill Practice - Page 280: 43

$|-3+10i|=\sqrt{109}$

#### Work Step by Step

The absolute value of a complex number $z=a+bi,$ denoted $|z|,$ is a nonnegative real number defined as $|z|=\sqrt{a^{2}+b^{2}}$. $|z|=|-3+10i|$ $=\sqrt{a^{2}+b^{2}}\qquad$ ...substitute $-3$ for $a$ and $10$ for $b$ $=\sqrt{(-3)^{2}+10^{2}}\qquad$ ...simplify. $=\sqrt{9+100}$ $=\sqrt{109}$

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