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

Sep 20, 2016

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

Explanation:

We require the denominator to be a real number. This can be achieved by multiplying the numerator/denominator by 3i.

$\frac{- 2 - 5 i}{3 i} \times \frac{3 i}{3 i} = \frac{- 6 i - 15 {i}^{2}}{9 {i}^{2}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \frac{- 6 i - 15 {i}^{2}}{9 {i}^{2}} = \frac{15 - 6 i}{- 9}$

and dividing.

$= \frac{15}{- 9} + \frac{- 6}{- 9} i = - \frac{5}{3} + \frac{2}{3} i$