# How do you write the following quotient in standard form -10/(2i)?

Aug 16, 2016

$5 i$

#### Explanation:

We require to express the fraction with a real denominator.

To achieve this make use of the following fact.

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

Multiply the numerator and denominator by i

$\frac{- 10}{2 i} \times \frac{i}{i} = \frac{- 10 i}{2 {i}^{2}} = \frac{- 10 i}{- 2} = 5 i$

$\Rightarrow - \frac{10}{2 i} = 5 i = 0 + 5 i \text{ in standard form}$