# How do you simplify (2+4i)/(2i)?

Sep 10, 2016

$2 - i$

#### Explanation:

First, rewrite the denominator in $a + b i$ form

$\frac{2 + 4 i}{0 + 2 i}$

Secondly, multiply by the numerator and denominator by the complex conjugate of the denominator as follows:

$\left(\frac{2 + 4 i}{0 + 2 i}\right) \left(\frac{0 - 2 i}{0 - 2 i}\right)$

Expand numerator and denominator.

$\frac{0 - 4 i + 0 i - 8 {i}^{2}}{0 - 0 i + 0 i - 4 {i}^{2}}$

Recall that ${i}^{2} = - 1$

$\frac{- 4 i + 8}{4} = \frac{- 4 i}{4} + \frac{8}{4} = - i + 2 = 2 - i$