# How do you simplify (4+9i)/(12i)?

Oct 4, 2016

$\frac{3}{4} - \frac{1}{3} i$

#### Explanation:

We require to make the denominator of the fraction real.

We can do this by multiplying numerator/denominator by i.

That is : $\frac{4 + 9 i}{12 i} \times \frac{i}{i} = \frac{4 i + 9 {i}^{2}}{12 {i}^{2}}$

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

$\Rightarrow \frac{4 i + 9 {i}^{2}}{12 {i}^{2}} = \frac{4 i - 9}{- 12} = \frac{- 9}{- 12} + \frac{4 i}{- 12}$

$\Rightarrow \frac{4 + 9 i}{12 i} = \frac{3}{4} - \frac{1}{3} i$