# How do you simplify 4/(7-9i)?

$= \frac{14}{65} + i \frac{18}{65}$
Multiply numerator and denominator by the conjugate of the denominator $7 + 9 i$
So the expressiion $= \frac{4 \left(7 + 9 i\right)}{\left(7 - 9 i\right) \left(7 + 9 i\right)} = \frac{28 + 36 i}{49 + 81} = \frac{28}{130} + \frac{36 i}{130} = \frac{14}{65} + \frac{18 i}{65}$
as ${i}^{2} = - 1$