# How do you write the complex conjugate of the complex number  sqrt(-15)?

Aug 1, 2016

$\overline{\sqrt{- 15}} = - \sqrt{15} i$

#### Explanation:

Given a complex number $a + b i$, the complex conjugate of that number, denoted $\overline{a + b i}$, is given by $\overline{a + b i} = a - b i$

In our case, then, we have

$\overline{\sqrt{- 15}} = \overline{\sqrt{15} i}$

$= \overline{0 + \sqrt{15} i}$

$= 0 - \sqrt{15} i$

$= - \sqrt{15} i$

Aug 1, 2016

$- \sqrt{15} i$

#### Explanation:

It's important to remember that ${i}^{2} = - 1$

This means we can rewrite

$\sqrt{- 15} \text{ as } \sqrt{15 {i}^{2}} = \sqrt{15} i$

For complex number $z = x + y i$ the complex conjugate $\overline{z}$ is defined as $\overline{z} = x - y i$

We have $z = 0 + \sqrt{15} i \implies \overline{z} = 0 - \sqrt{15} i$