You may want to review adding complex numbers first.
Multiplying complex numbers is also similar to multiplying polynomials. You multiply each term of one by each term of the other. For example, suppose you have to square 3 + 3i. This is (3 + 3i)(3 + 3i), so you get 9 + 9i + 9i + 9i2. The two 9i terms combine, giving us 9 + 18 + 9i2. If we were multiplying polynomials, we'd be done. In fact, there's just one more step; we need to take into account that i2 = −1. This means that our answer is 9 + 18i − 9, which simplifies to 18i.