complex exponential funcion

[chant]

Hi guys,

My problem is the following: I have to prove Cauchy-Riemann theorem for f(z)=e^(z-i).
According to Euler, this function is e^x(cosy+isiny)(cos1-isin1).

However, when I do the partial equation, they do not fit Cauchy-Riemann, so that means there is no derivative for the function. BUT derivative of e^x is always e^x, isn't it?

Are my partial derivative calculations wrong then? Or maybe transformations of the function in the first place?

Thanks for help.

 

[HallsofIvy]

chant, perhaps it would be better if you showed us what you did and how you determined that the C-R equations are NOT satisfied. I suspect you made an error differentiating. If we see what you did, we can point out the error.