Using only real arithmetic operations, write a computer program that, when given as input the real and imaginary parts (x, y) of z = x + iy, produces as output the real and imaginary parts of (a) e z...

Using only real arithmetic operations, write a computer program that, when given as input the real and imaginary parts (x, y) of z = x + iy, produces as output the real and imaginary parts of (a) e z , (b) sin z, and (c) cosh z. Use the polar form of the Cauchy-Riemann equations (Prob. 6 in Exercises 2.4) to give another proof of Theorem 4.