# Activities

• • • ##### Subject Area

• Math: Precalculus: Applications of Trigonometry

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

4.5

• ##### Report an Issue

Complex Number Multiplication

#### 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.