Complex Analysis L04: The Complex Logarithm, Log(z)

Описание: This video introduces the complex Logarithm, Log(z), as the inverse of the complex exponential. The Logarithm is a very important function that has infinitely many values in the complex plane. We also discuss branch cuts, and principle n-th roots.

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This video was produced at the University of Washington

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0:00 Defining the complex Logarithm
11:58 Plotting the complex Logarithm
16:26 Full formula for Log(z)
18:54 Recap/Summary
21:37 Branch cuts
23:12 Infinite spiral staircase of solutions
25:28 Teaser: Cauchy Integral Formula