The Origin of Complex Numbers and the Notation "I"

Build on your class' understanding of real numbers as they begin working with complex numbers. Pupils begin with an exploration of i and the patterns in the powers of i. After developing a definition for i, they...

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...

This quick set of problems provides a brief refresher on the arithmetic of complex numbers. Learners need to multiply, add and subtract, and remember features of i when raised to a power. Included solutions are clear enough that...

Sal solves a complex determinant problem from the 2010 IIT entrance test. Knowledge of determinants, the exponential form of complex numbers, trigonometric ratios, and algebraic thinking are all utilized here.

This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...

This video continues looking at dividing complex numbers by looking at the conjugate of a complex number. The instructor then uses the conjugate to rationalize the denominator of a rational expression with a complex number in the...

Sal discusses the usefulness of the conjugate of the complex number in this video. First, he shows how to add a complex number and its conjugate graphically and algebraically. Then, he shows how to simplify a rational expression with...

In this video, a complex number is defined and graphed on the complex plane. Sal also shows how to add, subtract, and multiply two complex numbers. He shows how to divide two complex numbers but runs out of time and continues in the...

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.

The foil method had been used for years as a way to remember how to simplify complex numbers. This process is demonstrated step-by-step, slowly so the learner will be able to follow along as the instructor solves the problem. Intended...