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. . . .

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Explore the properties of these two fascinating functions using trigonometry as a guide.

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.