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expand on equations 1 and 2

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see attached please expand on and explain the attached work

ie how does one make the transformations shown in equation 1 and 2 and 3...please show this work in complete, painful detail

I have given this as a new post as I believe it is outside the original post

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Solution Summary

The expert determines how one makes the transformations shown in equation 1 and 2.

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Problem:

There are 2 complex numbers Z that satisfy Z^n = 1 and {(Z+1)^n} =1 (n not equal to 0) for some positive integer n. Find Z.

Solution:

Every complex number z can be expressed in the exponential form
( 1)
which comes from the common algebraic form
( 2)
If we represent the complex number z in the xOy plane, we observe that
( 3)
so that the expression (2) becomes:
( 4)
Using ...

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