# How do you divide 3/(5i)?

#### Answer:

$\frac{3}{5 i} = \frac{3 {i}^{4}}{5 i} = \frac{3 {i}^{3}}{5} = - \frac{3}{5} i$

#### Explanation:

Keep in mind that $i = \sqrt{- 1}$ which means that ${i}^{2} = - 1$ and therefore ${i}^{4} = 1$. So we can rewrite the question as:

$\frac{3 {i}^{4}}{5 i} = \frac{3 {i}^{3}}{5}$

${i}^{3} = - \sqrt{- 1} = - i$ and so:

$\frac{3 {i}^{4}}{5 i} = \frac{3 {i}^{3}}{5} = - \frac{3}{5} i$

Sep 18, 2016

#### Answer:

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

#### Explanation:

To divide this fraction we require the denominator to be a real number.

This is achieved in this case by multiplying the numerator/denominator by i.

$\Rightarrow \frac{3}{5 i} = \frac{3}{5 i} \times \frac{i}{i} = \frac{3 i}{5 {i}^{2}}$

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

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