When dividing complex numbers, why do you need to multiply the numerator and
denominator by the complex conjugate of the
denominator?

Hope this helps..

Step-by-step explanation:  

So when you need to divide one complex number by another, you multiply the numerator and denominator of the problem by the conjugate of the denominator. This step creates a real number in the denominator of the answer, which allows you to write the answer in the standard form of a complex number.