# How do you write the complex conjugate of the complex number 8 + 4i?

Jul 1, 2016

$| 8 + 4 i | = 4 \sqrt{5}$

#### Explanation:

Given a complex number $a + b i$, the complex conjugate of that number, denoted $| a + b i |$, is given by

$| a + b i | = \sqrt{{a}^{2} + {b}^{2}}$

and represents the distance of that number from the origin on the complex plane.

In our case, then we have the complex conjugate of $8 + 4 i$ as

$| 8 + 4 i | = \sqrt{{8}^{2} + {4}^{2}} = \sqrt{64 + 16} = \sqrt{80} = 4 \sqrt{5}$