# What is the complex conjugate of 1 + sqrt( -50)?

Dec 8, 2015

#### Answer:

$1 - \left(5 \sqrt{2}\right) i$

#### 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 expression, $1 + \sqrt{- 50}$, does not appear to be in the $a + b i$ form of a complex number at first glance. However, $\sqrt{- 50} = \left(5 \sqrt{2}\right) i$.

Thus, the complex conjugate of $1 + \left(5 \sqrt{2}\right) i$ is $1 - \left(5 \sqrt{2}\right) i$.