# What is the complex conjugate of sqrt(-7)?

Dec 8, 2015

$- i \sqrt{7}$

#### Explanation:

To find a complex conjugate, simply change the sign of the imaginary part (the part with the $i$). This means that it either goes from positive to negative or from negative to positive.

As a general rule, the complex conjugate of $a + b i$ is $a - b i$.

Your case is seemingly odd, and may not seem to fit the pattern.

However, $\sqrt{- 7} = i \sqrt{7}$.

As such, this can be written in the $a + b i$ form of a complex number as $0 + i \sqrt{7}$.

Thus, the complex conjugate of $0 + i \sqrt{7}$ is $0 - i \sqrt{7}$, which equals $- i \sqrt{7}$.