Discuss, the analyticity of the following and for each function, describe where it is analytic and where it is not analytic: (a) f(x + y) = x²- y² + 2xyi (b) f(z) = |z| (c) f(z) = Im(z) == Find where the function h(z) = x3 + 3xy2-3x + i(y³ + 3x²y - 3y) is differentiable, and where it is analytic. Explain your answer.