# How do you find the absolute value of -9+6i?

Sep 25, 2016

$\sqrt{117}$

#### Explanation:

Given a complex number $z = x + y i$ then using Pythagoras' theorem, it's magnitude is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{| z | = | x + y i | = \sqrt{{x}^{2} + {y}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

here x = - 9 and y = 6

$\Rightarrow \sqrt{{\left(- 9\right)}^{2} + {6}^{2}} = \sqrt{81 + 36} = \sqrt{117} \text{ absolute value}$