Let f= u + iv be a continuous function and y(t) = x(t) + iy(t) be...

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Let f= u + iv be a continuous function and y(t) = x(t) + iy(t) be a piecewise smooth curve. Show that Re{f, f(z) dz} = f (u dx - v dy and Im {f, f(z) dz} = [ (v dx + u dy). Here, dx = x'(t) dt, dy = y'(t) dt. Let f= u + iv be a continuous function and y(t) = x(t) + iy(t) be a piecewise smooth curve. Show that Re{f, f(z) dz} = f (u dx - v dy and Im {f, f(z) dz} = [ (v dx + u dy). Here, dx = x'(t) dt, dy = y'(t) dt.

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