# How do you find abs(2 - 4i)?

May 29, 2016

$2 \sqrt{5}$

#### Explanation:

Given a complex number z = x + iy , then it's magnitude is found as follows

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

here x = 2 and y = -4

$\Rightarrow | 2 - 4 i | = \sqrt{{2}^{2} + {\left(- 4\right)}^{2}} = \sqrt{20} = 2 \sqrt{5}$