# How do you divide (5i)/(-2-6i)?

Nov 13, 2016

#### Answer:

$\frac{5 i}{- 2 - 6 i} = \frac{3}{4} - \frac{1}{4} i$

#### Explanation:

Whenever you divide a complex number by another complex number, you write it in fractional form

and then multiply numerator and denominator by complex conjugate of denominator

Complex conjugate of $a + b i$ is $a - b i$. Hence that of $- 2 - 6 i$ is $- 2 + 6 i$

So $\frac{5 i}{- 2 - 6 i} \times \frac{- 2 + 6 i}{- 2 + 6 i}$

= $\frac{- 10 i - 30 {i}^{2}}{{\left(- 2\right)}^{2} - {\left(6 i\right)}^{2}}$

as ${i}^{2} = - 1$, this becomes

$\frac{- 10 i + 30}{4 + 36} = \frac{30 - 10 i}{40} = \frac{3}{4} - \frac{1}{4} i$