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Powers and Roots of Complex Numbers

De Moivre's Theorem using polar form.

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Complex Number Theorems

Vocabulary

Fill in the equation for each theorem then describe each theorem in your own words.
Theorem Equation Description
Product Theorem __________________________ _________________________________________________
Quotient Theorem __________________________ _________________________________________________
De Moivre's Theorem __________________________ _________________________________________________

Practice

Product and Quotient Theorems

If  and  find:

.

Find the quotients

.
Click here for help with the Product and Quotient theorems.

.

Powers and Roots 

To find roots of complex numbers, you De Moivre's Theorem to creat the equation . This helps you find roots.

Remember: Numbers must be in polar form to use De Moivre's Theorem!

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Use De Moivre’s Theorem:

  1. Identify the 3 complex cube roots of 
  2. Identify the 4 complex fourth roots of 
.

Click here for answers.

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