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

• 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.

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

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.