Related Topics:

More Math Worksheets

More Printable Math Worksheets
Algebra II

There are three sets of complex numbers worksheets:

Examples, solutions, videos, and worksheets to help Algebra II students learn how to multiply complex numbers.

There are three sets of multiply complex numbers worksheets

- Multiply Complex Numbers (Monomials)
- Multiply Complex Numbers (Monomials & Binomials)
- Multiply Complex Numbers (Binomials)

In mathematics, the imaginary unit i is defined as the square root of -1. It is a fundamental concept in complex numbers. Powers of i repeat in a cyclic pattern, which makes them predictable. Here are the powers of i up to i^{5}:

- i
^{1}= i - i
^{2}= -1 (since i is square root of -1) - i
^{3}= -i (since i^{3}is the product of i^{2}and i) - i
^{4}= 1 (since i^{4}is the square of -1) - i
^{5}= i (since i^{5}is the product of i^{4}and i) The pattern repeats from i^{5}. i^{6}= i^{2}and so on.

**Multiply binomial complex numbers**

To multiply binomial complex numbers, you use the distributive property of multiplication over addition.

Here’s how you multiply two complex numbers (a + bi) and (c + di)

Distribute each term in the first binomial to each term in the second binomial:

(a + bi) · (c + di)

= a · c + a · di + c · bi + bi · di

= ac + adi + bci + bdi^{2}

= ac + adi + bci - bd

= ac - bd + (ad + bc)i

Example:

Multiply (2 + 3i) by (1 − 4i):

Use the distributive property to multiply the terms:

(2 + 3i) · (1 − 4i)

= (2 · 1) + (2 · -4i) + (3i · 1) + (3i · - 4i)

= 2 - 8i + 3i - 12i^{2}

= 2 - 5i - (-12)

= 14 - 5i

Have a look at this video if you need to review how to multiply complex numbers.

Click on the following worksheet to get a printable pdf document.

Scroll down the page for more **Complex Number Worksheets**.

**Printable**

(Answers on the second page.)

Complex Number Worksheet #1 (Monomials)

Complex Number Worksheet #2 (Monomials & Binomials)

Complex Number Worksheet #3 (Binomials)

**Online**

Powers of i: Positive Exponents

Powers of i: Negative Exponents

Complex Number Addition

Complex Number Subtraction

Complex Number Multiplication

Complex Number Division

Complex Number: Magnitude (Absolute Value)

Distance Between Two Complex Numbers

Midpoint of Two Complex Numbers)

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.