SOLVED: A complex function f(z) can be written in the Cartesian form as mappingf(z) = u(x, y) iv(x, y)with u(x, y) := Re(f(z)) and v(x, y) := Im(f(z)).Some complex functions f(z) are given by:(1) f(z) = e^z,(2) f(z) = z - i,(3) f(z) = Im(z) i.Find the mapping and for each of the above complex functions.Determine whether the following function is continuous at the point z = 0, where:f(z) = 1, if z ≠ 0, 0, if z = 0.Justify your conclusion.

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