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Complex Number Exponents of Euler’s Number

Complex Number Exponents of Euler’s Number. By Avinash Inabathula. Introduction. Reasons: Understanding math Aspirations ?. Introduction to e. Painted by Emanuel Handmann. Leonhard Euler (15 April 1707 – 18 September 1783) Jacob Bernoulli e≈ 2.7182818284….

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Complex Number Exponents of Euler’s Number

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  1. Complex Number Exponents of Euler’s Number By Avinash Inabathula

  2. Introduction • Reasons: • Understanding math • Aspirations • ?

  3. Introduction to e Painted by Emanuel Handmann • Leonhard Euler (15 April 1707 – 18 September 1783) • Jacob Bernoulli • e≈ 2.7182818284…

  4. Taylor Series == Wikipedia contributors. "Taylor series." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 27 Jan. 2010. Web. 30 Jan. 2010.

  5. Maclaurin Expansion ex eix eix = a+bi

  6. A Little Simplification sin(x) cos(x)

  7. Graphical Representation Unit Circle on complex plane Consider f(π): f(π) = i f(x)=eix = cos(x) + isin(x) = cos(π) + isin(π)= -1 b x b=0i • π 1 a=-1 a -i

  8. Review • In conclusion:

  9. Conclusion • Further derivations

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