University of Texas
Complex Numbers
Are complex numbers and binomials similar? This stack of slides provides an introduction to complex numbers and shows how to operate with them. The worked examples show a connection between operating with binomials and operating with...
EngageNY
An Appearance of Complex Numbers 2
Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews the...
Virginia Department of Education
Complex Numbers
Build on your class' understanding of real numbers as they begin working with complex numbers. Pupils begin with an exploration of i and the patterns in the powers of i. After developing a definition for i, they simplify complex number...
CK-12 Foundation
Trigonometric Form of Complex Numbers
Represent complex numbers in two ways. Pupils use the interactive to convert polar and rectangular representations of complex numbers. The learners drag an overlay back and forth over the coordinate plane to reveal the polar coordinates...
Alabama Learning Exchange
Imaginary Numbers? What Do You Mean Imaginary?
Don't worry, this resource actually exists. Scholars learn about imaginary numbers and work on problems simplifying square roots of negative numbers. As an extension, they research the history of imaginary numbers.
Curated OER
Complex Numbers
In this complex numbers worksheet, students write numbers in standard form. They identify real, imaginary and complex numbers. Students find the absolute value and conjugate of a number. This two-page worksheet contains 45 problems.
EngageNY
The Geometric Effect of Some Complex Arithmetic 1
Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into what it...
Curated OER
Complex Numbers
In this algebra worksheet, students solve complex numbers using multiplication and division properties. There are 10 questions with an answer key.
EngageNY
Discovering the Geometric Effect of Complex Multiplication
Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...
EngageNY
Complex Numbers as Solutions to Equations
Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex.
Curated OER
Complex Distance
Have learners graph complex numbers to gain a visual and mathematical understanding of the distance and the midpoint between two complex numbers. This lesson is short, but to the point, and addresses an important complex number concept....
Project Maths
Complex Number Operations
What do animated videos have to do with mathematics? Using operations of complex numbers and their representations on the complex plane, high schoolers observe how mathematics could be used to move animations. The lesson provides an...
EngageNY
Linear Transformations Review
Time for matrices and complex numbers to come together. Individuals use matrices to add and multiply complex numbers by a scalar. The instructional activity makes a strong connection between the operations and graphical transformations.
Curated OER
Complex numbers in polar form
Young scholars plot complex numbers in the polar plane. They convert complex numbers in polar form to rectangular form. Students plot coordinates in the polar plane. They plot complex numbers in the complex plane. Young scholars are...
Curated OER
Complex numbers in polar form
Students plot complex numbers in the polar plane. They are asked to list what they believe are the five most famous numbers in mathematics. Students are explained that generally accepted that the five most famous numbers in mathematics...
Mathematics Vision Project
Quadratic Equations
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
CK-12 Foundation
DeMoivre's Theorem and nth Roots: The nth Roots of Unity
The nth roots of unity all have a magnitude of one. Scholars use the unit circle and DeMoivre's Theorem to find the complex roots of one and discover that the complex numbers all lie on the unit circle and are equally spaced around it...
EngageNY
Mid-Module Assessment Task - Precalculus (module 1)
Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is the...
Curated OER
Radicals: Addition & Subtraction of Complex Numbers
In this radical worksheet, students simplify complex numbers. They find the sum and difference of complex numbers. This two-page worksheet contains 11 multiple-choice problems. Answers are given on the last page.
Math About
Introduction to Complex Numbers
In this complex number instructional activity, students explore the properties of imaginary numbers to find the square roots of negative numbers. Explanations and examples are given prior to the exercise. This two-page instructional...
Curated OER
Complex Analysis: Complex Numbers
In this complex numbers worksheet, students compute the value of given expressions and write the answer in complex number form. This one-page worksheet contains three equations.
Curated OER
Complex Analysis: Graphical Representations
In this graphical representation instructional activity, students draw an Argand diagram depicting complex numbers. They draw in vectors that represent complex numbers. This three-page instructional activity contains approximately ten...
EngageNY
The Geometric Effect of Multiplying by a Reciprocal
Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...
Curated OER
Complex Analysis: Polar & Exponential Forms
In this polar and exponential form worksheet, students use Euler's Formula to write complex numbers in exponential form. They write numbers in rectangular form. This two-page worksheet contains seven multi-step problems.