# How do you simplify (6-3i)/ (2+i)?

Dec 1, 2015

I found: $\frac{9}{5} - \frac{12}{5} i$
You need to change the denominator into a pure real and then divide. To do this you can multiply and divide by the complex conjugate of the denominator $2 - i$ to get:
$\frac{6 - 3 i}{2 + i} \cdot \frac{2 - i}{2 - i} =$
$= \frac{12 - 6 i - 6 i + 3 {i}^{2}}{4 + 1} =$ remembering that ${i}^{2} = - 1$
$= \frac{12 - 12 i - 3}{5} = \frac{9}{5} - \frac{12}{5} i$