# How do you simplify (-5 - 3i)/(4i)?

Jun 30, 2018

$- \frac{3}{4} + \frac{5}{4} i$

#### Explanation:

The convention is to not have irrational numbers in the denominator, so let's multiply the top and bottom by $4 i$.

$\frac{4 i \left(- 5 - 3 i\right)}{4 i \cdot 4 i}$

$= \frac{- 20 i - 12 {i}^{2}}{16 {i}^{2}}$

Recall that ${i}^{2} = - 1$. This now simplifies to

$\frac{- 20 i + 12}{-} 16$

We can factor out a $4$ in all terms to get

$\frac{- 5 i + 3}{-} 4$

This simplifies to

$- \frac{3}{4} + \frac{5}{4} i$

Hope this helps!