Complex Analysis: Holomorphic functions

So my teacher explained what holomorphic functions were today. But it did not make much sense.
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

holomorphic is another word for analytic - which means differentiable on some open set in the plane.

There is a difference between being analytic and being differentiable. For f to be analytic at a point z - it means that there is an open set containing x throughout which the function is differentiable. If you are differentiable ONLY at one point then you are NOT analytic.

f is differentiable at z iff the cauchy reimann equations are satisfied at that point. This is probably the easiest way to show a function is holomorphic.

mathwonk