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MAT 3730 Complex Variables

MAT 3730 Complex Variables. Section 1.4 The Complex Exponential. http://myhome.spu.edu/lauw. Preview. Extension of the exponential function to the complex numbers The Euler’s Formula The De Moivre’s Formula (du mwA´vru ). The Complex Exponential. The Complex Exponential.

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MAT 3730 Complex Variables

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  1. MAT 3730Complex Variables Section 1.4 The Complex Exponential http://myhome.spu.edu/lauw

  2. Preview • Extension of the exponential function to the complex numbers • The Euler’s Formula • The De Moivre’s Formula (du mwA´vru )

  3. The Complex Exponential

  4. The Complex Exponential

  5. Basic Property

  6. Basic Property

  7. Definition of eiy There are 2 ways to look at the definition of 1. Through the Maclaurin Series 2. Through the property

  8. Definition of eiy There are 2 ways to look at the definition of 1. Through the Maclaurin Series 2. Through the property

  9. Through the Maclaurin Series Suppose we want eiyto have the same Maclaurin series, then

  10. Through the Maclaurin Series Suppose we want eiyto have the same Maclaurin series, then

  11. Through the Maclaurin Series

  12. The Euler’s Formula

  13. Definition of Complex Exponential

  14. Example 1

  15. Example 2

  16. Properties of Complex Exponential

  17. Polar Form (Revisit)

  18. Example 3

  19. (du mwA´vru) Example 4 De Moivre’s Formula

  20. Example 5

  21. Next Class • Read Section 1.5 • We will look at how to find: • Powers zn • Roots z1/m

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