Question

How do you simplify `(2 -3i) / (5 + i)`?

Answer 1

The answer is `7/26 - 17/26 i`

Explanation:

Multiply the top (numerator) and bottom (denominator) by the complex conjugate of the bottom:

`(2-3i)/(5+i)=(2-3i)/(5+i) * (5-i)/(5-i) = (10-17i+3i^2)/(25-i^2)`

Now use the fact that `i^{2}=-1`:

`(2-3i)/(5+i)=(7-17i)/(25+1)=7/26 - 17/26 i`.