How do you divide imaginary numbers?

1 Answer
Apr 25, 2018

a+bic+di=ac+bdc2+d2+ibcadc2+d2

Explanation:

Suppose we wanted to determine

a+bic+di

We can multiply the numerator and denominator by the complex conjugate of the denominator. In this case the complex conjugate of the denominator is cdi.

a+bic+di=(a+bi)(cdi)(c+di)(cdi)

=acadi+bci+bdc2cdi+cdi+d2

=ac+bd+(bcad)ic2+d2

=ac+bdc2+d2+ibcadc2+d2