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

Sep 29, 2016

Multiply by the complex conjugate in both the numerator and denominator.

#### Explanation:

To simplify this expression, we need to remove the imaginary component in the denominator.

So, we multiply by the complex conjugate of $2 i$ which is $- 2 i$ on both the numerator and denominator

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

$\left(\frac{- 2 i}{- 2 i}\right)$ evaluates to 1, so multiplying by it does not change the value of our expression.

Multiplying through, we find $\frac{- 8 i - 8 {i}^{2}}{- 4 {i}^{2}}$

We know ${i}^{2} = - 1$, so we replace in the expression and get:

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

Since all terms have a 4, we can divide through by it, getting our answer:

$- 2 i + 2$