# How do you divide (-4-4i)/(4i)?

Jul 21, 2016

$- 1 + i$

#### Explanation:

We can multiply the top and bottom of a fraction by the same thing without changing the value of the fraction. Combining this with the fact that the product of a complex number with it's complex conjugate will be real gives us a handy trick for dividing by complex numbers - multiply numerator and denominator by the conjugate!

$\frac{- 4 - 4 i}{4 i} \cdot \frac{- 4 i}{- 4 i}$

$= \frac{16 i + 16 {i}^{2}}{- 16 {i}^{2}}$

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

$= \frac{16 i - 16}{16} = - 1 + i$