# How do you simplify (1-2i)/(3-4i)?

Mar 9, 2018

$\frac{- 2 i + 11}{25}$

#### Explanation:

Multiply by the conjugate of $\frac{3 + 4 i}{3 + 4 i}$ to cancel out the imaginary numbers in the denominator. Also remember that ${i}^{2}$ is equal to -1.

$= \frac{1 - 2 i}{3 - 4 i} \cdot \frac{3 + 4 i}{3 + 4 i}$
$= \frac{3 + 4 i - 6 i - 8 {i}^{2}}{9 + 12 i - 12 i - 16 {i}^{2}}$
$= \frac{- 2 i + 3 - 8 \left(- 1\right)}{9 - 16 \left(- 1\right)}$
$= \frac{- 2 i + 11}{25}$