determine analytic function $f$ if $|f|=(x^2+y^2)e^x$

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I'm self-studying complex analysis. Could someone please help me get this problem started?

I know an analytic function will satisfy the Cauchy-Riemann equations, but I only know the modulus of the function. I have no idea how to proceed

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Hint: $x^2 + y^2 = |z^2|$, and $e^{x} = |e^z|$, where $z = x+iy$.