Question

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

Answer 1

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

`((6-3i)(2-i))/((2+i)(2-i))=(12-6i-6i+3i^2)/(4-i^2)=`

But we know that `i^2=-1`, then

`(9-12i)/(4+1)=9/5-12/5i`