# How do you simplify (5 + 8i) /( 6- i)?

Nov 21, 2015

$\frac{22}{37} + \frac{53}{37} i$

#### Explanation:

Multiply the conjugate.

$\frac{5 + 8 i}{6 - i} \times \frac{6 + i}{6 + i} = \frac{30 + 5 i + 48 i + 8 {i}^{2}}{36 + 6 i - 6 i - {i}^{2}} = \frac{30 + 53 i + 8 {i}^{2}}{36 - {i}^{2}}$

Remember that because $i = \sqrt{1} , {i}^{2} = - 1$.

$\frac{30 + 53 i + 8 \left(- 1\right)}{36 - \left(- 1\right)} = \frac{30 - 8 + 53 i}{36 + 1} = \frac{22 + 53 i}{37} = \frac{22}{37} + \frac{53}{37} i$

Note that I've written the answer in the complex form $a + b i$.