# How do you simplify (2 -3i) / (5 + i) ?

Nov 11, 2015

The answer is $\frac{7}{26} - \frac{17}{26} i$

#### Explanation:

Multiply the top (numerator) and bottom (denominator) by the complex conjugate of the bottom:

$\frac{2 - 3 i}{5 + i} = \frac{2 - 3 i}{5 + i} \cdot \frac{5 - i}{5 - i} = \frac{10 - 17 i + 3 {i}^{2}}{25 - {i}^{2}}$

Now use the fact that ${i}^{2} = - 1$:

$\frac{2 - 3 i}{5 + i} = \frac{7 - 17 i}{25 + 1} = \frac{7}{26} - \frac{17}{26} i$.