# How do you simplify 2 + 7i div 1-3i?

$\frac{2 + 7 i}{1 - 3 i}$
Multiply and divide by $1 + 3 i$.
$\implies \frac{2 + 7 i}{1 - 3 i} = \frac{\left(2 + 7 i\right) \left(1 + 3 i\right)}{\left(1 - 3 i\right) \left(1 + 3 i\right)} = \frac{2 + 6 i + 7 i + 21 {i}^{2}}{1 - 9 {i}^{2}} = \frac{2 + 13 i - 21}{1 + 9} = \frac{- 19 + 13 i}{10} = - \frac{19}{10} + \frac{13 i}{10}$
$\implies \frac{2 + 7 i}{1 - 3 i} = - \frac{19}{10} + \frac{13 i}{10}$