Determine the largest set on which the function is analytic.
f(z) = (z2-2)e-xe-iy
f(x+iy) = U(x,y) + iV(x,y)
The Attempt at a Solution
I think I'm right in saying that f(z) is analytic if the CR equations (provided above) are satisfied.
So I would write f(z) as f(x+iy) to find U and V.
f(x+iy) = (x2-y2+i2xy-2)e-xeiy
This is where I am up to. I can't seem to think of how to split this into parts with and without i. (The exponential with i is what throws me).
Any advice on where to go next?