# How do you divide  (1-3i)/(2-7i)?

Jan 30, 2016

$\frac{23}{53} + \frac{1}{53} i$

#### Explanation:

Given:$\text{ } \frac{1 - 3 i}{2 - 7 i}$

Multiply by 1 in the form of: $\frac{2 + 7 i}{2 + 7 i}$

$\frac{\left(1 - 3 i\right) \left(2 + 7 i\right)}{\left(2 - 7 i\right) \left(2 + 7 i\right)}$

$\frac{2 + 7 i - 6 i - 21 {i}^{2}}{{2}^{2} - 49 {i}^{2}}$

but ${i}^{2} = - 1 \text{ so } - 49 {i}^{2} = + 49$

$\frac{23 + i}{53} \to \frac{23}{53} + \frac{1}{53} i$