# How do you write the complex conjugate of the complex number sqrt( -7) ?

Jul 26, 2016

$- \sqrt{- 7}$ or $- \sqrt{7} i$

#### Explanation:

If $a$ and $b$ are Real numbers then the Complex conjugate of $a + b i$ is $a - b i$.

By definition and convention, if $a$ is a negative number, then:

$\sqrt{a} = \sqrt{- a} i$

So:

$\overline{\sqrt{- 7}} = \overline{\sqrt{7} i} = - \sqrt{7} i = - \sqrt{- 7}$