# How do you divide i/(-2-8i)?

Nov 24, 2016

$- \frac{2}{17} - \frac{1}{34} i$

#### Explanation:

You can multiply both the terms of the fraction by $- 2 + 8 i$:

$\frac{i \left(- 2 + 8 i\right)}{\left(- 2 - 8 i\right) \left(- 2 + 8 i\right)}$

$\frac{- 2 i + 8 {i}^{2}}{4 - 64 {i}^{2}}$

and, since ${i}^{2} = - 1$,

$\frac{- 2 i - 8}{4 + 64}$

$= \frac{- 2 i - 8}{68}$

or, in the standard form:

$- \frac{8}{68} - \frac{2 i}{68} = - \frac{2}{17} - \frac{1}{34} i$