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6.6

6.6. De Moivre’s Theorem and n th Roots. 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

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6.6

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  1. 6.6 De Moivre’s Theorem and nth Roots

  2. 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 zn = c, n is an integer and c is a complex number.

  3. Complex Plane

  4. Absolute Value (Modulus) of a Complex Number

  5. Graph of z = a + bi

  6. Trigonometric Form of a Complex Number

  7. Example Finding Trigonometric Form

  8. Example Finding Trigonometric Form

  9. Product and Quotient of Complex Numbers

  10. Example Multiplying Complex Numbers

  11. Example Multiplying Complex Numbers

  12. A Geometric Interpretation of z2

  13. De Moivre’s Theorem

  14. Example Using De Moivre’s Theorem

  15. Example Using De Moivre’s Theorem

  16. Example Using De Moivre’s Theorem

  17. nth Root of a Complex Number

  18. Finding nth Roots of a Complex Number

  19. Example Finding Cube Roots

  20. Example Finding Cube Roots

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