# DeMoivre's Theorem and nth Roots

## Raise complex numbers to powers or find their roots.

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Practice DeMoivre's Theorem and nth Roots

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Polar Theorems

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### Theorem Overview

##### In your own words, describe each theorem as it relates to polar equations.
 Theorem Description Product Theorem ________________________________________________________________ Quotient Theorem ________________________________________________________________ DeMoivre's Theorem ________________________________________________________________

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##### Complete the theorems:

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Where  and let  be a positive integer.

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The general rule for finding the  roots of a complex number if  is _____________________________________________ (Hint: start wth DeMoivre's Theorem).

### Practice

Multiply each pair of complex numbers. If they are not in trigonometric form, change them before multiplying.

Divide each pair of complex numbers. If they are not in trigonometric form, change them before dividing.
Use DeMoivre's Theorem to evaluate each expression. Write your answer in standard form.

Find the principal fifth roots of each complex number. Write your answers in standard form.

Solve each equation.