Sal solves the problem x^3 = 1 for all of the real and complex roots using the exponential form of the complex number. He shows how the roots found in exponential form are the same as those in a more traditional form of a complex number...

This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a...

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.

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...

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...

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...

How does the Fundamental Theorem of Algebra apply to equations with complex roots? Using recently learned concepts about the complex plane, learners determine all the complex roots of polynomials. They can find the same roots as...

Multiplying complex numbers geometrically is complicated. Find an easier way with a short video that explains the process of multiplying complex numbers on the complex plane. The connection with the process and the angles and moduli sets...

How do addition and subtraction work on the complex plane? A short video presentation provides a clue on how to add complex numbers geometrically. The video ends with four problems to determine the rules for multiplication on the complex...

If the square root of negative one exists, where is it on the number line? A math video presents a geometric representation of complex numbers and the complex plane, and then compares it to the geometric representation of real numbers —...

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...

Tying together an introductory unit on polar coordinates, graphs, and vectors is often a daunting task. So many nuanced math skills develop through these lessons that making sure an assessment hits them is difficult, to say the least....

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...

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...

High schoolers participate in a role-play activity to determine how to replace heat shields on the space shuttle using polar coordinates.

Complex numbers have two parts and can be graphed on a complex plane. After an explanation of the complex plane, this video shows three examples of graphing complex numbers.

The class examines graphs in the form r = F(¿¿) in polar coordinates (r, ¿¿), in particular with the circle, ellipse and other conic sections. They determine the nature of an ellipse by studying the role of the semimajor axis and...

In this complex logarithm activity, 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. ...

In this function worksheet, students evaluate problems involving functions, identify the domain and range of functions, and complete inversion mapping. This two-page worksheet contains approximately twelve problems.

In this complex plane worksheet, students describe definitions words relating to a complex plane and point sets. They give examples for each definition. This two page worksheet contains thirteen problems.

In this point set worksheet, students explore definitions describing planar point sets. They use the definitions to describe examples of point sets. This two-page worksheet contains four problems and 15 definitions.