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

Jul 27, 2016

$- 4 - 9 i$

#### Explanation:

To eliminate the i from the denominator of the fraction multiply numerator and denominator by i . This will leave a real number on the denominator.

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

$\Rightarrow \frac{9 - 4 i}{i} \times \frac{i}{i} = \frac{i \left(9 - 4 i\right)}{i} ^ 2 = \frac{9 i - 4 {i}^{2}}{i} ^ 2 = \frac{4 + 9 i}{- 1}$

$\Rightarrow \frac{9 - 4 i}{i} = - 4 - 9 i$