Dont know if this is thr correct place to put this but im looking for a couple of pointers on a recent maths quiz i got.

I have to integrateZe^(z^2)around simple closed curve C C: from 1 along axis from i to i.

I understand that you must check to see if the function is analytic before deciding which method of integration to use but i seem to becoming unstuck with my partial derivatives. Here's what i've done

f(z) = Ze^(z^2)

as z = x+iy

=> f(z) = (x + iy)e^((x+iy)^2)

f(z) = xe^((x+iy)^2) + iye^((x+iy)^2)

let u(x,y) = xe^((x+iy)^2) let v(x,y) = iye^((x+iy)^2)

do i need to use the product rule to find Ux and Vy?