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DeMoivre's Theorem and nth Roots

Raise complex numbers to powers or find their 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 ________________________________________________________________

.

Complete the theorems:

Product Theorem

 ____________________________________

.

Quotient Theorem

 ____________________________________

.

DeMoivre's Theorem

 ____________________________________

Where  and let  be a positive integer.

.

 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.

Click here for more help with equations using DeMoivre's Theorem.

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