Differentiating Trigonometric Identities Cos z and Sin z for Complex z

Fortunately for students, the differentials of complex functions follow the same rules as for real functions, but for different reasons. In this video we show why d/dz (cos z) = - sin z and vice versa for complex 'z', with help from the hyperbolic functions sinh z and cosh z, as well as the Cauchy Riemann equations.