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## Homework Statement

Determine the largest set on which the function is analytic.

f(z) = (z

^{2}-2)e

^{-x}e

^{-iy}

## Homework Equations

z=x+iy

f(x+iy) = U(x,y) + iV(x,y)

U

_{x}=V

_{y}

U

_{y}=-V

_{x}

## 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) = (x

^{2}-y

^{2}+i2xy-2)e

^{-x}e

^{iy}

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?

Thanks