Education Technology

Complex Number Multiplication

Updated on 07/30/2015

Activity Overview

This lesson involves the product of complex numbers, powers of i and complex conjugates.

Objectives

  • Students will compute the product of two complex numbers.
  • Students will discover the pattern in powers of the imaginary number i.
  • Students will compute the product of complex conjugates and relate this value to the absolute value of the original complex number.
  • Students will graph complex numbers in polar form.
  • Students will compute the product of complex numbers in polar form.

Vocabulary

  • complex conjugate
  • absolute value
  • magnitude
  • argument
  • polar form

About the Lesson

This lesson involves the product of complex numbers, powers of i and complex conjugates.
As a result students will:

  • Compute the product of two complex numbers and write a general symbolic result for the product.
  • Discover the pattern in powers of i and simplify i raised to any power.
  • Compute the product of complex conjugates and relate this to the absolute value of the original complex number.
  • Visualize the product of complex numbers written in polar form and write the product in polar form.