# How do you find the absolute value of -3+10i?

Nov 13, 2016

$\sqrt{109}$

#### Explanation:

Given a complex number $z = x + y i$

Then, using the theorem of Pythagoras, the absolute value is.

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

here x = - 3 and y = 10

$\Rightarrow | - 3 + 10 i | = \sqrt{{\left(- 3\right)}^{2} + {10}^{2}} = \sqrt{109}$