# What is the complex conjugate of sqrt(-15)?

Oct 29, 2015

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

#### Explanation:

If $x \ge 0$, then $\sqrt{x}$ means the non-negative square root of $x$.

If $x < 0$ then $\sqrt{x} = i \sqrt{- x}$

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

The complex conjugate is formed by replacing $i$ with $- i$, so the complex conjugate of $\sqrt{- 15} = i \sqrt{15}$ is $- \sqrt{- 15} = - i \sqrt{15}$