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

Feb 14, 2016

Multiply by 1, written as the complex conjugate of the bottom of the fraction divided by itself, in this case $\frac{1 - 2 i}{1 - 2 i}$:

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

#### Explanation:

Multiply top and bottom of the fraction by the complex conjugate of the bottom. For a complex expression $a + b i$ the complex conjugate is $a - b i$.

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

While simplifying, remember ${i}^{2} = - 1$

$= \frac{2 - i + 6}{1 + 4} = \frac{8 - i}{5}$