# How do you divide (6+8i)/(9i)?

Feb 22, 2017

I got: $\frac{8}{9} - \frac{2}{3} i$

#### Explanation:

We need first to change the denominater into a real number by multiplying and dividing by $9 i$:

$\frac{6 + 8 i}{9 i} \cdot \frac{9 i}{9 i} = \frac{54 i + 72 {i}^{2}}{81 {i}^{2}} =$

remembering that ${i}^{2} = - 1$ we get:

$\frac{54 i - 72}{- 81} = - \frac{54 i}{81} + \frac{72}{81} = \frac{8}{9} - \frac{2}{3} i$