Zeros

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Convergence

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Complex Variables. 1.2

What are all possible solutions of z^4 + 4 = 0? From this information, write out a complete factorization of z^4 + 4.

Simplify the Complex Expression : Five Questions

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Hint: First consider what curve z...

Compute: lim as r -> infinity |f(z)|, where z = re^[(i)("alpha")] Your answer will depend on "alpha". Hint: First consider what curve z = re^[(i)("alpha")] traces out in the complex plane as r -> infinity

Radius of Convergence : Summations and Power Series

Please see the attached file for full problem description. a) Evaluate b) What is the radus of convergence .... .... To what simple function does this series converge? c) Is f(z)=... ... analytic near z= -1? and expand f(z)= ... in a power series near z= -1 can we predict the domain of convergence from the outset?

Fourier Series Proof

Please see the attached file for full problem description. Q = e^ (i n pi alpha) + e^ (-i n pi alpha) and Q = 0. How can Q be two different things?

Example of a non-rectifiable closed Jordan curve.

Give an example of a non-rectifiable closed Jordan curve on the interval -1<=t<=1. My thought: t + i(sin 1/t) + ????? Please advise what curve I can add to make this work. Or, if this will not work, please provide an example of a non-rectifiable closed Jordan curve on -1<=t<1.

Complex Variables

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Complex Variables 115

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