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Transformation and Mapping

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Using the exponential form {see attachment} of z, how that the transformation {see attachment} which is the sum of the identity transformation and the transformation discussed in the attachment, map circles ...

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Solution Summary

This is a proof regarding transformations and mapping circles onto ellipses.

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Let's take the circle equation in terms of complex functions:
( 1)
and let's apply the given mapping:
( 2)
( 3)
we need to highlight the real and imaginary part in (2):
( 4)

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