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...

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.

Consider complex numbers, roots, and quadratic equations. Use the discriminate as a way to determine the nature of a quadratic's roots. Then discuss the similarities and differences between quadratics with two, one, or no real roots....

The class explores the concept of complex numbers on a website to generate their own Mandelbrot sets. They will practice performing operations with complex numbers and then to get a visual understanding, graph the absolute value of a...

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. 

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.

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...

In this algebra worksheet, young scholars solve 16 problems involving imaginary numbers. In the first three, students find the square root of 3 negative numbers in terms of i. Nine problems involve addition, subtraction, multiplication...

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...

For this complex numbers worksheet, learners classify numbers, perform operations on complex numbers, and find complex solutions to equations, in sixty-eight problems.

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...

Students 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. Students are asked to...

In this complex numbers worksheet, students solve problems involving polynomials, real constants containing imaginary numbers, and find the complex number that satisfies a given equation. This two-page worksheet contains seven problems.

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. 

A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...

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...

Use tables, graphs, and substitution to solve systems of linear equations. An envelope of sample problems is passed around the classroom, and each learner has the opportunity to solve the system in the envelope. This is a great way to...

Students solve problems with complex numbers. In this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.

Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson plan asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and...

The 15th segment in a series of 22 uses examples that present proportional relationships with fractions. Pupils work through the problems and discover that the process is the same as it is with whole number values. Graphing the...

Review the multiple methods of solving quadratic equations through an analysis of the discriminant. Scholars use the discriminant to determine the best solution method and then solve various equations. As a challenge, learners build...

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....