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 + 3*i*.
This is (3 + 3*i*)(3 + 3*i*), so you get 9 + 9*i* +
9*i* + 9*i*^{2}. The two 9*i* terms
combine, giving us 9 + 18 + 9*i*^{2}. If we
were multiplying polynomials, we'd be done. In fact, there's just
one more step; we need to take into account
that *i*^{2} = −1. This means that our answer
is 9 + 18*i* − 9, which simplifies to 18*i*.