Complex sine

Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.

Problem

Show that the complex solutions of $\sin z = 2$ are given by $$z = {\pi \over 2} - i \log (2\pm\sqrt 3) +2n\pi.$$