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The Domain of a Complex Function

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For each of the functions below, describe the domain of definition that is understood:
a) f(z)=1/(z^2+1)
b) f(z)=Arg(1/z)
c) f(z)=z/(z+z bar)
d) f(z)=1/(1-|z|^2 )

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Solution Summary

This solution helps go through how to find the domain of different complex functions within the context of complex analysis.

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The main idea on these is to exclude complex numbers that result in a zero denominator which is not defined. The attachment will provide rational for each of these and describe the excluded numbers geometrically on the complex plane.

a) f(z)=1/(z^2+1) In this case z^2=-1 will result in a zero denominator ...

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