How do you find the absolute value of -7-2i?

Apr 2, 2017

$\left\mid - 7 - 2 i \right\mid = \sqrt{53}$

Explanation:

The absolute value of a complex number is essentially its (Euclidean) distance from $0$, which we can find with the help of Pythagoras.

$\left\mid x + i y \right\mid = \sqrt{{x}^{2} + {y}^{2}}$

So in our example:

$\left\mid - 7 - 2 i \right\mid = \sqrt{{\left(- 7\right)}^{2} + {\left(- 2\right)}^{2}} = \sqrt{49 + 4} = \sqrt{53}$