# How do you simplify 2/(4-9i)?

Feb 27, 2016

$\frac{8 + 18 i}{97}$

#### Explanation:

When you have a complex number in the numerator you have to multiply by the conjugate:

$\frac{2}{4 - 9 i} \cdot \frac{4 + 9 i}{4 + 9 i}$

$\frac{8 + 18 i}{{4}^{2} + {9}^{2}}$

$\frac{8 + 18 i}{97}$

97 is a prime number, so we cannot simplify the fraction.