Multiplying

Multiply complex numbers the way you multiply two brackets: every term of one times every term of the other. For (2 + i)(3 + 4i) that gives 6 + 8i + 3i + 4i^2.

Now the one new step: i^2 = -1, so 4i^2 is -4. The line becomes 6 + 11i - 4, and collecting gives 2 + 11i.

Why replace i^2? It is a real number in disguise, and replacing it is what brings the answer back to the form a + bi. Watch the signs: a product like 3i × (-2i) is -6i^2, which is +6.