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# DeMoivres Theorem - PowerPoint PPT Presentation

DeMoivre's Theorem. Lesson 5.3. Using Trig Representation. Recall that a complex number can be represented as Then it follows that What about z 3 ? . DeMoivre's Theorem. In general (a + b i ) n is Apply to Try . Using DeMoivre to Find Roots. Again, starting with a + b i =

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## PowerPoint Slideshow about 'DeMoivres Theorem' - jovan

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### DeMoivre's Theorem

Lesson 5.3

• Recall that a complex number can be represented as

• Then it follows that

• In general (a + bi)n is

• Apply to

• Try

• Again, starting with a + bi =

• also works when n is a fraction

• Thus we can take a root of a complex number

• Note that there will be n such roots

• One each for k = 0, k = 1, … k = n – 1

• Find the two square roots of

• Represent as z = r cis θ

• What is r?

• What is θ?

• Solutions are:

Roots will be equally spaced around a circle with radius r1/2

Graphical Interpretation of Roots

• Consider cube root of 27

• Using DeMoivre's Theorem

Roots will be equally spaced around a circle with radius r1/3

• Recall that one method of solving polynomials involves taking roots of both sides

• x4 + 16 = 0x4 = - 64

• Now we can determine the roots(they are all complex)

Try out spreadsheet for complex roots

• Lesson 5.3

• Page 354

• Exercises 1 – 41 EOO