Question

How do you divide `(-4-4i)/(4i)`?

Answer 1

`-1+i`

Explanation:

We can multiply the top and bottom of a fraction by the same thing without changing the value of the fraction. Combining this with the fact that the product of a complex number with it's complex conjugate will be real gives us a handy trick for dividing by complex numbers - multiply numerator and denominator by the conjugate!

`(-4-4i)/(4i)*(-4i)/(-4i)`

`=(16i + 16i^2)/(-16i^2)`

Recall that `i^2 = -1`

`=(16i - 16)/(16) = -1 + i`