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.