# How do you simplify -9-9i div -1-8i?

Apr 15, 2016

$- 9 - 9 i \div - 1 - 8 i = \textcolor{g r e e n}{\frac{81}{65} - \frac{63}{65} i}$

#### Explanation:

$- 9 - 9 i \div - 1 - 8 i = \frac{- 9 - 9 i}{- 1 - 8 i}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{- 9 - 9 i}{- 1 - 8 i} \cdot \frac{- 1 + 8 i}{- 1 + 8 i}$

$\textcolor{w h i t e}{\text{XXX}} \frac{9 + 9 i - 72 i + 72}{1 + 64}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{81 - 63 i}{65}$

Apr 15, 2016

−9−9i div −1−8i=81/65-63/65i

#### Explanation:

−9−9i div −1−8i can be written as (−9−9i)/(−1−8i)

To simplify we need to multiply numerator and denominator by the complex conjugate of the denominator.

Complex conjugate of a number $a + b i$ is $a - b i$,

hence in above case one needs to multiply by $- 1 + 8 i$

Hence (−9−9i)/(−1−8i)

= ((−9−9i)xx(-1+8i))/((−1−8i)xx(-1+8i))

= $\frac{9 - 72 i + 9 i - 72 {i}^{2}}{{\left(- 1\right)}^{2} - {\left(8 i\right)}^{2}}$

= $\frac{9 - 72 i + 9 i - 72 \left(- 1\right)}{1 - 64 \left(- 1\right)}$

= $\frac{9 - 72 i + 9 i + 72}{1 + 64}$

= $\frac{81 - 63 i}{65}$

= $\frac{81}{65} - \frac{63}{65} i$