How do you find the absolute value of 1+3i?

Mar 9, 2018

$\left\mid 1 + 3 i \right\mid = \sqrt{10}$

Explanation:

The absolute value of a complex number is its distance from the origin $0$ in the complex plane.

By Pythagoras' theorem this is the square root of the sum of the squares of the real and imaginary parts.

That is:

$\left\mid 1 + 3 i \right\mid = \sqrt{{1}^{2} + {3}^{2}} = \sqrt{1 + 9} = \sqrt{10}$