To divide two complex numbers, multiply both the numerator and the denominator of the fraction by the
conjugate of the denominator.
The conjugate of the complex number a + bi is the complex number a - bi.
Denominator: -1 + 5i ---> Conjugate: -1 - 5i
[ (2 - 3i) / (-1 + 5i) ] · [ (-1 - 5i) / (-1 - 5i) ] = [ (2 - 3i) · (-1 - 5i) ] / [ (-1 + 5i) · (-1 - 5i) ]
Now, you'll need to multiply: (2 - 3i) · (-1 - 5i) [this will be the numerator of your answer]
and you'll need to multiply: (-1 + 5i) · (-1 - 5i) [this will be the denominator of your answer]
The denominator will no longer contain any "i" terms; it will just be a regular, real, number.