Table of Contents |
A complex number is a number in the form , containing both a real part and an imaginary part. The imaginary part is followed by i, which is the imaginary unit, .
Recall the following formulas for imaginary numbers:
When multiplying complex numbers, we follow a similar process when multiplying binomial factors we may be familiar with when studying quadratics. The multiplication process is often referred to as FOIL, which distributes terms into the factors being multiplied. Let's take a moment to review FOIL with real numbers before looking at examples of complex number multiplication.
FOIL stands for First, Outside, Inside, Last, and refers to terms that are multiplied together to form individual addends to the product.
EXAMPLE
MultiplyMultiply first terms: | |
Multiply outside terms: | |
Multiply inside terms: | |
Multiply last terms: | |
Combine like terms | |
Our solution |
When multiplying two complex numbers, we will be following the same procedure but will need to make an additional consideration when the imaginary unit is squared.
When multiplying complex numbers, we'll want to consider the imaginary unit, i.
EXAMPLE
Multiply the complex numbersMultiply first terms: | |
Multiply outside terms: | |
Multiply inside terms: | |
Multiply last terms: | |
Combine like terms | |
Simplify |
Rewrite as -6 | |
Combine like terms | |
Our solution |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License