Complex Numbers - Multiplication

Complex Numbers
Multiplication

A couple of days ago I introduced complex numbers, and we learned how to raise the complex number i to any power. You can see that post here: Complex Numbers – Examples and Powers of i

Yesterday we reviewed how to add and subtract complex numbers, and I gave you a problem to try involving subtraction. You can see that post here: Complex Numbers – Addition and Subtraction

Today I will go over how to multiply complex numbers. But first I will provide a solution to yesterday’s problem. Here is the problem one more time, followed by a solution:

Example: When we subtract 2 – 3i from –5 + 6i we get what complex number?

Solution: (–5 + 6i) – (2 – 3i) = –5 + 6i – 2 + 3i = –7 + 9i.

Multiplication

We can multiply two complex numbers by formally taking the product of two binomials and then replacing i² by –1. That process leads to the following formula:

(a + bi)(c + di) = (ac – bd) + (ad + bc)i

Example: Compute (2 – 3i)(–5 + 6i)

I will provide a solution to this question tomorrow. Meanwhile, please post your attempted solutions in the comments below.

For those of you that prefer videos…