Complex numbers and algebra

Complex numbers of the form a+bi are mostly introduced these days in the context of quadratic equations, but according to Stillwell cubic equations are closer to their historical roots. We show how the cubic equation formula of del Ferro, Tartaglia and Cardano requires some understanding of complex numbers even when only real zeroes appear to be involved. The use of imaginary numbers in calculus manipulations is illustrated with some computations of Johann Bernoulli relating the inverse tan function to co