# How do you divide (2+3i)/(1+2i)?

Feb 8, 2016

Rationalise the denominator to find:

$\frac{2 + 3 i}{1 + 2 i} = \frac{8}{5} - \frac{1}{5} i$

#### Explanation:

Multiply both numerator and denominator by the Complex conjugate $1 - 2 i$ of the denominator as follows:

$\frac{2 + 3 i}{1 + 2 i} = \frac{\left(2 + 3 i\right) \left(1 - 2 i\right)}{\left(1 + 2 i\right) \left(1 - 2 i\right)}$

$= \frac{2 - 4 i + 3 i - 6 {i}^{2}}{1 + 4}$

$= \frac{8 - i}{5}$

$= \frac{8}{5} - \frac{1}{5} i$