Simplify: 3+i/-3+i

Answer 1

To simplify (or perform the division), we multiply top and bottom by the conjugate of the bottom. The conjugate is the same terms but we switch one of the signs. So the conjugate of "-3 + i" is "-3 - i". So:

Answer 2

(3+i)/(-3+i)

Factor out the negative.

-(3+i)/(3-i)

Multiply by the conjugate

-(3+i)(3+i)/(3-i)(3+i)

Simplify

-(8+6i)/10

Reduce

-(4+3i)/5 ■