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As I am attempting to do my homework, I realized that I still dont really know what a Holomorphic function is, let alone how to show that one is.

The questions looks like this:

show that f(z)=u(z)+iv(z) is holomorphic or not;

where u and v are given different values throughout the problem.

I was hoping someone could clarify what a holomorphic function is, and maybe show me a little trick as to how I should go about this problem.

Thanks