While solving it using the definition of norm I got $\exp{2x}$ where $x=\mathfrak{R}(z)$. If I changed the integration to polar coordinate I was not able to do further.
We are being asked to find the solution in terms of Bessel's function which includes $J_1(2i)$. Reverse solving it using it's integral representation I was getting $0$ value.
Give some hints to proceed.
Thank you.