It is with a deep sense of loss and regret that we let you know about the death of Michael Deakin on 5 August 2014. Michael contributed enormously to mathematics enrichment in Australia over several decades.
Back in 2005, I devoted two of these columns to the history of complex and imaginary numbers. Here I return to the theme, but take a different slant on it, telling how an initially suspect notion became respectable.
It is natural to look for relationships between the roots of a polynomial and the coefficients.
Q1451 Use the ideas of the solution to problem 1443 (later this issue) to find without calculus the maximum value of \[ \frac{x}{(x^2 + a^2)^2}, \] where $a$ is a positive real number.
We begin with the solution to problem 1440 from volume 49, issue 3, which was inadvertently omitted last issue.
Q1440 Let $f(x)$ be a polynomial with degre 2012, such that \[ f(1) = 1,\quad f(2) = \frac{1}{2},\quad f(3) = \frac{1}{3},\ldots, f(2013) = \frac{1}{2013}.\]