How do you simplify (4+ 2i) /( -1 + i)?

1 Answer
May 2, 2018

(4+2i)/(-1+i) | *(-1-i)

((4+2i)(-1-i))/((-1+i)(-1-i))

(-2i^2-6i-4)/(1-i^2)

(2-6i-4)/(1+1)

(-2-6i)/(2)

=-1-3i

Explanation:

We want to get rid of i in the the bottom of the fraction in order to get it on Certesian form. We can do this by multiplying with (-1-i).

This will give us,

((4+2i)(-1-i))/((-1+i)(-1-i))

(-2i^2-6i-4)/(1-i^2)

Out from here we know that i^2=-1 and -i^2=1. So we can get rid of the i^2 too. Leaving us to

(-2-6i)/(2)

=-1-3i