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

Jun 27, 2018

See explanation below

#### Explanation:

We will use the conjugate of complex number in denominator

$2 - i$. We multiply and divide by this number, so the quotient does not varies

$\frac{\left(6 - 3 i\right) \left(2 - i\right)}{\left(2 + i\right) \left(2 - i\right)} = \frac{12 - 6 i - 6 i + 3 {i}^{2}}{4 - {i}^{2}} =$

But we know that ${i}^{2} = - 1$, then

$\frac{9 - 12 i}{4 + 1} = \frac{9}{5} - \frac{12}{5} i$