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.
This article introduces complex numbers, brings together into one
bigger 'picture' some closely related elementary ideas like vectors
and the exponential and trigonometric functions and their
derivatives and proves that e^(i pi)= -1.