# Residues and Poles; Polar Numbers; Demoivre's Theorem

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Please see the attachment for questions relating to residues and poles (polar numbers and Demoivre's Theorem).

These problems are from complex variable class. Please specify the terms that you use if necessary and clearly explain each step of your solution.

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#### Solution Preview

See attached

(a) We know that

Here, f(z) = , z0 = -1

Therefore,

But any polar number z can be written as z = r(cos +i sin )

To write in polar form, i = r(cos +i sin ...

#### Solution Summary

The residues and poles using Demoivre's Theorem is discussed. Complex variable classes are analyzed.

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