Question

How do you divide imaginary numbers?

Answer 1

`(a+bi)/(c+di)=(ac+bd)/(c^2+d^2)+i(bc-ad)/(c^2+d^2)`

Explanation:

Suppose we wanted to determine

`(a+bi)/(c+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 `c-di`.

`(a+bi)/(c+di)=((a+bi)(c-di))/((c+di)(c-di))`

`=(ac-adi+bci+bd)/(c^2-cdi+cdi+d^2)`

`=(ac+bd+(bc-ad)i)/(c^2+d^2)`

`=(ac+bd)/(c^2+d^2)+i(bc-ad)/(c^2+d^2)`