**Example 1**: Divide the complex numbers, .

The first step is to write the original problem in fractional form.

Since our denominator is , its conjugate is equal to . Remember to change only the sign of the imaginary term to get the conjugate.

We take this conjugate, and use it as the common multiplier of both the numerator and denominator.

From here, we just need to multiply the numerators together and the denominators as well. Use the FOIL Method when multiplying the binomials. Perform all necessary simplifications to get the final answer.

Don't forget to use the fact that .