2. show that the function f(z) = zez is entire by verifying that the real and imaginary parts of f satisfy the cauchy- riemann equations at each point of the co

2. Show that the function f(z) = zez is entire by verifying that the real and imaginary parts of f satisfy the Cauchy- Riemann equations at each point of the complex plane. What is the anti-derivative of f? IfC is any contour extending from z = 0 to z = in, find the value of the integral fz)dz. Also, use the ML-inequality to prove that where C is the positively oriented circle |z| = 1/2.