# What is the complex conjugate of (2 - 4i)?

Nov 7, 2015

It is: $2 + 4 i$

#### Explanation:

The complex conjugate is the number with equal real part and imaginary part equal in magnitude but opposite in sign and have the interesting property that when multipyed together they give a pure real number:

in our case you have:

$\left(2 + 4 i\right) \left(2 - 4 i\right) = 4 \cancel{- 8 i} \cancel{+ 8 i} - 16 {i}^{2} = 4 + 16 = 20 =$Real;

using the fact that ${i}^{2} = - 1$.