Consider the complex function

f(z) = $\displaystyle e^{-iz}$.

(a) Express f(z) in the form u(x, y) + iv(x, y), give u and v.

(b) Use the Cauchy-Riemann equations and the existence and continuity of the partial derivatives of u and v to show that f '(z) exists for all z.

(c) Using your results from b), find an expression for f '(z) in terms of z.

Help with this question please, Thanks.