Provide STEP BY STEP solution with explanation and formulas on how you proceeded to the next step.

Consider the equations. o f (z) dz = plu(x, y) + iv(x,y)] (dx + idy) of (2)dz = $ [u(x, y) dx - v(x, y ) dy ] + [v(x, y) dx + u(x, y) dy] Where the first term is the real part and the second term is the imaginary part. This is an example of a proof of Cauchy integral theorem. 1. Prove that for analytic f (z), Im[f f(z)dz] = 0. (This is the imaginary part)