# How do you divide  (6-10i) / (7-2i) ?

Dec 18, 2015

Multiply both numerator and denominator by the Complex conjugate of the denominator and simplify to find:

$\frac{6 - 10 i}{7 - 2 i} = \frac{62}{53} - \frac{58}{53} i$

#### Explanation:

$\frac{6 - 10 i}{7 - 2 i}$

$= \frac{\left(6 - 10 i\right) \left(7 + 2 i\right)}{\left(7 - 2 i\right) \left(7 + 2 i\right)}$

$= \frac{\left(6\right) \left(7\right) + \left(6\right) \left(2 i\right) + \left(- 10 i\right) \left(7\right) + \left(- 10 i\right) \left(2 i\right)}{{7}^{2} + {2}^{2}}$

$= \frac{42 + 12 i - 70 i + 20}{49 + 4}$

$= \frac{62 - 58 i}{53}$

$= \frac{62}{53} - \frac{58}{53} i$