Copyright © 2011 Pearson, Inc. 6.6 De Moivre’s Theorem and nth Roots.

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Presentation transcript:

Copyright © 2011 Pearson, Inc. 6.6 De Moivre’s Theorem and nth Roots

Copyright © 2011 Pearson, Inc. Slide What you’ll learn about The Complex Plane Trigonometric Form of Complex Numbers Multiplication and Division of Complex Numbers Powers of Complex Numbers Roots of Complex Numbers … and why The material extends your equation-solving technique to include equations of the form z n = c, n is an integer and c is a complex number.

Copyright © 2011 Pearson, Inc. Slide Complex Plane

Copyright © 2011 Pearson, Inc. Slide Absolute Value (Modulus) of a Complex Number

Copyright © 2011 Pearson, Inc. Slide Graph of z = a + bi

Copyright © 2011 Pearson, Inc. Slide Trigonometric Form of a Complex Number

Copyright © 2011 Pearson, Inc. Slide Example Finding Trigonometric Form

Copyright © 2011 Pearson, Inc. Slide Example Finding Trigonometric Form

Copyright © 2011 Pearson, Inc. Slide Product and Quotient of Complex Numbers

Copyright © 2011 Pearson, Inc. Slide Example Multiplying Complex Numbers

Copyright © 2011 Pearson, Inc. Slide Example Multiplying Complex Numbers

Copyright © 2011 Pearson, Inc. Slide A Geometric Interpretation of z 2

Copyright © 2011 Pearson, Inc. Slide De Moivre’s Theorem

Copyright © 2011 Pearson, Inc. Slide Example Using De Moivre’s Theorem

Copyright © 2011 Pearson, Inc. Slide Example Using De Moivre’s Theorem

Copyright © 2011 Pearson, Inc. Slide Example Using De Moivre’s Theorem

Copyright © 2011 Pearson, Inc. Slide nth Root of a Complex Number

Copyright © 2011 Pearson, Inc. Slide Finding nth Roots of a Complex Number

Copyright © 2011 Pearson, Inc. Slide Example Finding Cube Roots

Copyright © 2011 Pearson, Inc. Slide Example Finding Cube Roots

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