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
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...
Curated OER
Polar and Cartesian Coordinates
The class has a brief review of polar and Cartesian coordinates. Then they get to play battleship and discover polar coordinates in more depth. They get a lot of practice converting from polar to Cartesian coordinate points and vice...
EngageNY
Distance and Complex Numbers 2
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...
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...
Texas Instruments
Complex Numbers: Plotting and Polar Form
Explore the concept of, and use the Ti-Nspire to, convert complex numbers into polar form. Then practice graphing complex numbers in the polar coordinate plane.
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...
Curated OER
Complex Analysis: Point Sets in the Complex Plane
In this complex plane learning exercise, students describe definitions words relating to a complex plane and point sets. They give examples for each definition. This two page learning exercise contains thirteen 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...
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
Justifying the Geometric Effect of Complex Multiplication
The 14th activity 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...
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...
Curated OER
Introduction to Polar coordinates
The class practices plotting points in a Cartesian coordinate system and a Polar coordinate system. They convert from one system to the other to get coordinates to plot. Then they play a Tic-Tac-Toe or Connect Four game to have a...
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...
Curated OER
Math 312 Spring 2004: Complex Logarithm
In this complex logarithm worksheet, students complete complex logarithm problems. They identify image and pre-image sets, indicate the location of the solution in a complex plane and give examples of integers with given parameters. ...
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....
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,...
Curated OER
Real and Complex Conjugates
Students explore examples of real binomial conjugates involving the square root of negative one. In a class setting, students study examples of complex conjugates and work given problems. They play "Find My Conjugate" game where real and...