Fourier series

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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. Thanks.

Complex Variables

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Complex Variables 115

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Complex Variables 2.2.17

Find the limit of f(z) = x^2/(x^2+y^2) +2i Where z=x+iy and |z| --> 0

Complex variables 3.3.11

Please see the attached file for full problem description. --- Show all steps, even minor details Send response as attachment Provide common sense explanations Determine a branch of log that is analytic at z = -1, and find its derivative there.

Locate all zeros and singularities

Locate all zeros and singularities for each of the attached functions.

Complex Variable; Uniformly Continous; Lipshitz Function; Cauchy Sequence

Please answer the attached complex variable problems. Thank you.

Evaluate Complex Variable (Contour; Circular Arc)

Please evaluate the attached variable (problem includes: contour and circular arc) Thank you.

Complex Variable (Circle; Contour)

For the attached problem, please use the theorem explained in the document to establish the indicated estimate.