# How do you simplify (5-3i)/(1+2i)?

Nov 20, 2015

$\frac{5 - 3 i}{1 + 2 i} = - \frac{1 + 13 i}{5}$

#### Explanation:

To simplify a fraction with a complex number in the denominator, we simply multiply the numerator and the denominator by the complex conjugate of the denominator.

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

Note that this will leave us with a real number for the denominator.

$\frac{5 - 3 i}{1 + 2 i} \cdot \frac{1 - 2 i}{1 - 2 i} = \frac{5 - 10 i - 3 i - 6}{1 - 2 i + 2 i + 4} = - \frac{1 + 13 i}{5}$