Imaginary numbers are a real thing. Scholars learn about complex numbers, real numbers, and imaginary numbers. They classify given numbers as strictly complex, strictly real, or strictly imaginary in an individual or group activity.

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...

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...

Conjugating in the math classroom — and we're not talking verbs! The seventh lesson plan in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to find the...

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...

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...

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....

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.

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...

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...

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...

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...

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...

Complex doesn't have to mean harder! Learners experiment with online software to determine the quadratic equations with complex solutions. They use the quadratic formula to solve equations with both real and complex solutions.

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...

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...

Help the class find a better way. Pupils recall finding nth roots or a complex number in polar form from a previous module to find the square root of a complex number. Using the second installment in a series of 23, scholars discover it...

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...

Go around and around on the complex plane. The sixth lesson plan 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...

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...

Take a step back to Algebra II. The first lesson in a series of 23 asks scholars to remember working with quadratic equations with complex solutions. Pupils apply polynomial identities to complex numbers and work examples that show how...

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...

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...

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...