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

Jan 27, 2016

$\frac{4}{5} - \frac{2}{5} i$

#### Explanation:

Remember: ${i}^{2} = - 1$

Given $\frac{2 - 4 i}{4 - 3 i}$

We can simplify this expression by multiply by the conjugate of the denominator

((2-4i)/(4-3i))color(red)(( (4+3i)/(4+3i))

Expand the expression, then combine like terms,

$\frac{8 + 6 i - 16 i - 12 {i}^{2}}{16 - 12 i + 12 i - 9 {i}^{2}}$

$= \frac{8 - 16 i - 12 \left(- 1\right)}{16 - 9 \left(- 1\right)}$

$= \frac{20 - 10 i}{25}$

$= \frac{20}{25} - \frac{10}{25} i$

$= \frac{4}{5} - \frac{2}{5} i$