How do you divide complex numbers?

Question

What's 3 -i/1 + 2i?

Answer 1

Multiply the fraction by 1... in the form a / a, where a is the conjugate of the denominator

In your example, the denominator is 1 + 2i. Its conjugate is 1 - 2i. Multiply top and bottom by that.

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

Simplifying:
(1 - 7i) / (5) =
1/5 - 7/5 i

Answer 2

You multiply the fraction by something called the conjugate which is the found by taking the denominator and changing the sign between the two terms. In this case, you would change 1+2i to 1-2i. Now, put 1-2i/1-2i which is another name for 1. When you multiply by 1, the value of the fraction does not change, so you are allowed to do the following.
the orgininal fraction multiplied by the conjugate/conjugate.

(3-i)/(1+2i) * (1-2i)/(1-2i)=multiply the numerators, then denominators.
(3-i)(1-2i)= 3-6i-1i+2i^2= 3-7i-2 since i^2 = -1, 1-7i
(1+2i)(1-2i)= 1 -2i+2i-4i^2=1+4=5

So, answer is (1-7i)/5

Answer 3

= (3-i)(1-2i)/ 5 ( multiplying by the conjugate=
=(3-6i-i -2)/5 = (1-7i)/5

Answer 4

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

:)








Doubt that's right...