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Lesson Plan
EngageNY

Roots of Unity

For Teachers 11th - 12th Standards
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....
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Lesson Plan
EngageNY

Curves in the Complex Plane

For Teachers 11th - 12th Standards
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...
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Interactive
CK-12 Foundation

Find Imaginary Solutions: Imaginary Zeros

For Students 10th - 12th Standards
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.
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Interactive
CK-12 Foundation

DeMoivre's Theorem and nth Roots: The nth Roots of Unity

For Students 11th - Higher Ed
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...
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Interactive
CK-12 Foundation

Trigonometric Form of Complex Numbers

For Students 11th - Higher Ed Standards
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...
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Assessment
EngageNY

Mid-Module Assessment Task - Precalculus (module 1)

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Complex Numbers as Vectors

For Teachers 11th - 12th Standards
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...
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Assessment
EngageNY

End-of-Module Assessment Task — Precalculus (Module 1)

For Teachers 11th - 12th Standards
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,...
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Lesson Plan
EngageNY

Exploiting the Connection to Trigonometry 1

For Teachers 11th - 12th Standards
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex number. Groups...
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Lesson Plan
EngageNY

Representing Reflections with Transformations

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Discovering the Geometric Effect of Complex Multiplication

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Trigonometry and Complex Numbers

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Distance and Complex Numbers 2

For Teachers 11th - 12th Standards
Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th lesson in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a formula to find...
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Lesson Plan
EngageNY

The Geometric Effect of Some Complex Arithmetic 2

For Teachers 11th - 12th Standards
The 10th activity 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...
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Lesson Plan
EngageNY

The Geometric Effect of Some Complex Arithmetic 1

For Teachers 11th - 12th Standards
Translating complex numbers is as simple as adding 1, 2, 3. In the ninth instructional activity in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads...
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Lesson Plan
EngageNY

An Appearance of Complex Numbers 1

For Teachers 11th - 12th Standards
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....
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Lesson Plan
EngageNY

Exploiting the Connection to Trigonometry 2

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

The Geometric Effect of Multiplying by a Reciprocal

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Justifying the Geometric Effect of Complex Multiplication

For Teachers 11th - 12th Standards
The 14th lesson in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship for the...
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Lesson Plan
EngageNY

Distance and Complex Numbers 1

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

Complex Number Division 2

For Teachers 11th - 12th Standards
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...
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Lesson Plan
EngageNY

An Appearance of Complex Numbers 2

For Teachers 11th - 12th Standards
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...
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Worksheet
Kuta Software

Imaginary Numbers

For Students 9th - 12th Standards
Here is a worksheet that takes all aspects of quadratic functions and incorporates imaginary numbers into the problems. The problems range from simplifying to graphing and solving by using a variety of methods with imaginary and complex...
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Lesson Plan
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Project Maths

Complex Number Operations

For Teachers 10th - 12th Standards
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 plan provides an...