# How do you simplify (9-i)/(2-i)?

Aug 10, 2018

$\frac{19 + 7 i}{5}$ or $\frac{19}{5} + \frac{7 i}{5}$

#### Explanation:

$\frac{9 - i}{2 - i}$

Multiply both numerator and denominator by the denominator's conjugate (2+i) to remove the $i$ from the denominator:
$\frac{9 - i}{2 - i} \textcolor{b l u e}{\cdot \frac{2 + i}{2 + i}}$

Simplify using FOIL:
$\frac{18 \cdot + 9 i + - 2 i + - {i}^{2}}{4 + 2 i + - 2 i + - {i}^{2}}$

Combine like terms. We also know that ${i}^{2}$ is $- 1$, so:
$\frac{18 + 7 i - \left(- 1\right)}{4 - \left(- 1\right)}$

Simplify:
$\frac{18 + 7 i + 1}{4 + 1}$

$\frac{19 + 7 i}{5}$

Hope this helps!