# How do you simplify (-2-5i)/(3i) ?

Apr 21, 2016

Multiply by $\frac{i}{i}$, eliminating $i$ from the denominator to find

$\frac{- 2 - 5 i}{3 i} = - \frac{5}{3} + \frac{2}{3} i$

#### Explanation:

To remove the imaginary component from the denominator, we can multiply the numerator and the denominator by $i$ and then simplify from there.

$\frac{- 2 - 5 i}{3 i} = \frac{\left(- 2 - 5 i\right) \cdot i}{3 i \cdot i}$

$= \frac{- 2 i - 5 {i}^{2}}{3 {i}^{2}}$

$= \frac{5 - 2 i}{- 3}$

$= - \frac{5}{3} + \frac{2}{3} i$