# Complex Analysis: Research

## Homework Statement

This isn't a standard homework problem. We were asked to do research and to find a theorem of the form:
If something about the partial derivatives of u and v is true then the implication is ##D(u,v)## at ##(x_0,y_0)## exists from ##R^2## to ##R^2##

## The Attempt at a Solution

I've done a lot of reading on the the difference in differentiability between ##R^2## and ##\mathbb{C}## but haven't been lucky enough to stumble upon an exact theorem. Anyway, a push in the right direction would save me a lot of time.

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Svein
A little hint: In ℝ2 , you may calculate the partial derivatives $\frac{\partial u}{\partial x}, \frac{\partial u}{\partial y}, \frac{\partial v}{\partial x}, \frac{\partial v}{\partial y}$ and you do not expect any obvious relation between them. On the other hand, in ℂ, you expect the derivative of f(z) to be just a function of z and nothing else.