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## C. Results from Analytic Function Theory

### C.4 Functions of a Complex Variable

In the sequel, we will let denote a complex variable. Note that is not the argument in the Z-transform, as used at other points in the book. Also, a function of a complex variable is equivalent to a function . This will have real and imaginary parts and respectively.

We can thus write

 (C.4.1)

Note that we also have

We then see that the previous results are immediately applicable to the real and imaginary parts of integrals of this type.

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