GATE2020-ME-1: 36

Question

An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as
$$f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$$
where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).