if z = x + iy
prove:z = re^(iθ) also work
Also,prove: dz= e^(iθ) dr + ire^(iθ)dθ
again from polar for of z dz = [ cos(theta) + i sin(theta) ] dr + r [-sin(theta) + i cos(theta)] d(theta)
dz = [ cos(theta) + i sin(theta) ] dr + i r [ cos(theta) + i sin(theta)] d(theta) that gives required result