Given \(f\left( z \right) = g\left( z \right) + h\left( z \right)\), where f, g, h are complex valued functions of a complex variable z. which one of the following statements is TRUE?

• A. If \(f\left( z \right)\) is differential at \({z_0}\), then \(g\left( z \right)\) and \(h\left( z \right)\) are also differentiable at \({z_0}\).
• B. If \(g\left( z \right)\) and \(h\left( z \right)\) are differentiable at \({z_0}\), then \(f\left( z \right)\) is also differentiable at \({z_0}\).
• C. If \(f\left( z \right)\) is continuous at \({z_0}\), then it is differentiable at \({z_0}\).
• D. If \(f\left( z \right)\) is differentiable at \({z_0}\), then so are its real and imaginary parts.