Question

How do you divide `(-3+10i)/(-6i)`?

Answer 1

`(-10-3i)/6=-5/3-1/2i`

Explanation:

`frac{-3+10i}{-6i}`

Multiply by the conjugate of the denominator over itself.
A conjugate of a complex number `a+bi` is `a-bi`.
The denominator can be written as `0-6i`, so the conjugate is `0+6i` or `6i`

`frac{(-3+10i)}{-6i}*(6i)/(6i)`

Distribute in the numerator and multiply in the denominator.

`frac{-3*6i +10i*6i}{-36i^2}`

`frac{-18i+60i^2}{-36i^2}`

Recall that `i^2=-1`

`frac{-18i+60(-1)}{-36(-1)}`

`(-18i-60)/36`

Factor out a 6 in both numerator and denominator.

`frac{6(-3i-10)}{6(6)}`

`frac{cancel(6)(-3i-10)}{cancel(6)(6)}`

`(-3i-10)/6` or

`(-10-3i)/6= -10/6-(3i)/6=-5/3-i/2=-5/3-1/2i`