Complex Derivative

[Crzyrio]

Hey Guys,


CUrrently doing an self teach online course in Complex Analysis and having a bit of trouble.


Where is the function f(z) = e^(^x^2-y^2) (cos(2xy) + isin(2xy)) analytic?
Find an expressing for f'(z) and give the derivative at i.


I know I have to use Cauchy-Riemann Equations but not sure what to do after that.


partial u/ partial x = e^(x^2-y^2)(xcos(2xy) - ysin(2xy))[/TEX]


partial v/ partial y = e^(x^2-y^2)(xcos(2xy) - ysin(2xy))


So the Cauchy-Riemann Equations are satisfied, does this mean it is analytic everywhere?


Also How would I go about finding the derivative? A tip in the right direction would be more than enough.


Thanks
RIoch

 

[pka]

Where is the function
f(z) = e^(^x^2-y^2) (cos(2xy) + isin(2xy)) analytic?
Find an expressing for f'(z) and give the derivative at i.

I am going to do the partial derivatives here. They are too awful.
But you find where \(\displaystyle u_x=v_y~\&~v_x=-u_y\).
Then the derivative \(\displaystyle f'(z)=u_x(x,y)+iv_x(x,y).\)