Operations with Complex Numbers Worksheets

Printable complex numbers worksheets:
Add & Subtract Complex Numbers
Multiply Complex Number
Rationalize Complex Number
Operations with Complex Numbers
Quadratic Equation with Complex Solutions

Examples, solutions, videos, and worksheets to help Algebra II students learn how to add, subtract and multiply complex numbers. How to represent a complex number on the complex plane and how to equate complex numbers.

Operations with Complex Numbers

Complex numbers are in the form
𝑧 = 𝑎 + 𝑏𝑖, where:
𝑎 is the real part, and 𝑏 is the imaginary part, with
𝑖 = √−1.

Representation of a Complex Number
A complex number 𝑧 = 𝑎 + 𝑏𝑖 is plotted as the point (𝑎,𝑏) on the complex plane:
𝑎 is the distance along the real axis (horizontal axis).
𝑏 is the distance along the imaginary axis (vertical axis).

Here are the common operations with complex numbers:

1. Addition and Subtraction
   Add or subtract the real parts and the imaginary parts separately.
2. Multiplication Use the distributive property and simplify using 𝑖² = −1.

Equating Complex Numbers
Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. If 𝑧₁ = 𝑎 + 𝑏𝑖 and
𝑧₂ = 𝑐 + 𝑑𝑖, then:
𝑧₁ = 𝑧₂ ⇔ 𝑎 = 𝑐 and 𝑏 = 𝑑

Have a look at this video if you need to review some complex numbers operations.

• Operations With Complex Numbers

Click on the following worksheet to get a printable pdf document.
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More Operations with Complex Numbers Worksheets

Printable
(Answers on the second page.)
Complex Plane Worksheet
Operations with Complex Numbers Worksheet #1 (addition & subtraction)
Operations with Complex Numbers Worksheet #2 (multiplication)
Operations with Complex Numbers Worksheet #3 (multiplication)
Equating Complex Numbers

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)

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Operations with Complex Numbers

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