How would I know if the function is entire?
This function is bounded, so if it was entire then it would be a constant.
This is a contradiction so it is not entire.
Polynomials are always entire.(ii) f(z) =
Check the Cauchy-Riemann equations(iii) f(z) = f(x + iy) = x
Polynomials are always entire.(iv) f(z) = 2.