What does it mean for a complex function to have no derivative?

Question

anonymous · Answer

The example I'm thinking of is$$z* conjugate(z)$$, where there is no (I read) derivative. But http://www.wolframalpha.com/input/?i=%28x%2Biy%29*%28x-iy%29 the function doesn't seem evil. Why is it that it has no derivative? Would you have to take the gradient to get something meaningful?

anonymous · Answer

doesn't the conjugate of z imply that there is an imaginary number involved?

anonymous · Answer

And while we're at it, on an unrelated note: is there a shorthand notation for 'converges' or 'diverges'?

anonymous · Answer

Sorry, I meant to say z=x+iy

anonymous · Answer

Wouldn't your function just yield a number?

anonymous · Answer

Yes, but the function has no (except at dx and dy and 0) derivative, and while I see why mathematically, I don't really understand it.

anonymous · Answer

Actually, In asking the question I answered it for myself. Thanks anyway.