EngageNY
Distance and Complex Numbers 1
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
EngageNY
Curves in the Complex Plane
Go around and around on the complex plane. The sixth lesson in a 23-part unit reviews representing numbers in the complex plane. Pupils graph numbers with equal moduli and notice they represent a circle. They continue to explore complex...
EngageNY
Trigonometry and Complex Numbers
Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the argument...
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
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...
EngageNY
Complex Numbers as Vectors
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
EngageNY
An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
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 Number Division 2
Individuals learn to divide and conquer complex numbers with a little help from moduli and conjugates. In the second lesson on complex number division, the class takes a closer look at the numerator and denominator of the multiplicative...
EngageNY
The Geometric Effect of Some Complex Arithmetic 2
The 10th lesson in a series of 32, continues with the geometry of arithmetic of complex numbers focusing on multiplication. Class members find the effects of multiplying a complex number by a real number, an imaginary number, and another...
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...
EngageNY
Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
EngageNY
Exploiting the Connection to Cartesian Coordinates
Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...
EngageNY
End-of-Module Assessment Task — Precalculus (Module 1)
A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...
EngageNY
Complex Numbers and Transformations
Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...
EngageNY
Roots of Unity
Visualize the nth roots of unity. Pupils calculate the nth roots of unity and find all n roots. Learners plot the solutions in the complex plane and observe that they are the vertices of a regular n-gon inscribed in the unit circle....
CK-12 Foundation
Find Imaginary Solutions: Imaginary Zeros
The resource is the real deal. Individuals investigate the imaginary zeros of f(x) = x^2 + 1. They accomplish this task by using an interactive that shows input values x = a + bi and output values x^2 + 1 on a complex plane.
Thomson Brooks-Core
Complex Numbers
A straightforward approach to teaching complex numbers, this lesson addresses the concepts of complex numbers, polar coordinates, Euler's formula, De moivres Theorem, and more. It includes a practice problems set with odd answers and a...
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...
EngageNY
Exploiting the Connection to Trigonometry 2
The class checks to see if the formula for finding powers of a complex number works to find the roots too. Pupils review the previous day's work and graph on the polar grid. The discussion leads the class to think about how to reverse...
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...
Colorado Unit Writing Project
Simple Machines
Planning an elementary science unit has never been simpler! These twelve lessons guide young scientists through an exploration of simple machines and their many uses in the real world before asking them to apply their learning in the...
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...
EngageNY
A Surprising Boost from Geometry
Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication.