Find the analytic function whose imaginary part is ݒ=

For each of the given functions find the set of points on which the Cauchy-Riemann equations aresatisfied. Also, check whether the function is analytic or not on the points where Cauchy-Riemannequations are satisfied.(a) 𝑓 (𝑧) = |𝑧|2

Find nonzero complex numbers z such that z¯=iz2

when we say a function is analytic

or each of the given functions find the set of points on which the Cauchy-Riemann equations aresatisfied. Also, check whether the function is analytic or not on the points where Cauchy-Riemannequations are satisfied.(a) 𝑓 (𝑧) = |𝑧|2(b) 𝑓 (𝑥 + 𝑖𝑦) = 𝑥3 + 𝑖(𝑦 − 1)3

Find the Z-transform of 𝒏𝒄𝒐𝒔(𝒏 𝜽)