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

1 Answer
Oct 15, 2016

(-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