De Moivre’s Theorem

De Moivre’s Theorem

If

and

is a natural number, then

Expressed in sines and cosines, this says that

In particular, if

, then

This theorem can be proved using the method of mathematical induction.

See Examples 1 – 2, pages 636 – 637, of the textbook

roots of

We can use De Moivre’s Theorem to find all the the

roots of a complex number
For a natural number

, we say that

is an

root of

Root Theorem

For

a positive number greater than 1

are the

distinct roots of

, and there are no other roots

     See Example 3, page 638, of the textbook

     Solving a Cubic Equation –
                                                       See Example 4, pages 638 - 639, of the textbook

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