Let's do it algebraically first, and let's take specific complex numbers to multiply, say 3 + 2i and 1 + 4i. Each has two terms, so when we multiply them, we'll get four terms: (3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i2. Now the 12i + 2i simplifies to 14i, of course.
