De Moivre, Trig Identities, Sine and Cosine in Terms of Exponentials by
Video Lecture 16 of 26
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### Lecture Description

Complex Analysis, Video 16 (Complex Arithmetic, Part 16). Application of De Moivre's Formula to Deriving Trigonometric Identities. Application of Euler's Formula to derive Exponential Representations of Cosine and Sine Functions.

Details: Review De Moivre's formula. Review application to trig identities. Mention mistake in previous video (#15) where I forgot to get rid of the "I" for the sine trigonometric identity. Derive another trigonometric identity by using (cos(theta)+i*sin(theta))^4 = cos(4theta)+i*sin(4theta) and the binomial theorem. Verbal mistake at 2:05: the second term in the binomial expression is NOT squared to get the second term in the expansion. Use Euler's formula in two ways to derive alternative representations of cos(theta) and sin(theta) in terms of exponentials involving the imaginary unit i.

### Course Description

This is a mini crash course providing all you need to know to understand complex numbers, and study Complex Analysis. Mathematica is used to help visualize the complex plane.