Evaluate G(w)=(∫_-z^z)(1/(2*π)√(,4-ε2)/(w-ε+𝑖*δ))*(d^)(ε) for δ→0 numerically and plot the real and imaginary parts as a function of w. If you are brave, you can try to evaluate by residues as well. But that is not needed now. Plot results for -5≤w≤5.