Chapter H, Problem 49E

If u(x) = f(x) + ig(x) is a complex-valued function of a real variable x and the real and imaginary parts f(x) and g(x) are differentiable functions of x, then the derivative of u is defined to be u′(x) = f′(x) + ig′(x). Use this together with Equation 7 to prove that if F(x) = e^rx, then F′(x) = re^rx when r = a + bi is a complex number.