We defined the hyperbolic functions of a complex variable and proved a variety of their properties. We then discussed inverse functions in general, then specifically the inverse function of e^z, first as a multivalued function log(z), then a specific `branch' called Log(z), and then a general way to define branches from log(z). We derived the derivatives of these branches; they are all 1/z. HW: section 31, 32, 35