More than 50 years ago when I was studying to become an electrical engineer, I came across complex numbers, which were used to represent out-of-phase voltages and currents using the j operator. I believe that the letter j was used, rather than i, because the latter stood for electrical current. So from the very start of my studies I had a clear mental picture of the imaginary unit as a rotational operator which could advance or retard electrical quantities in time.

When events dictated that I would pursue a career in computer programming— rather than electrical engineering—I had no need for complex numbers, until Mandlebrot’s work on fractals emerged. But that was a temporary phase, and I never needed to employ complex numbers in any of my computer graphics software. However in 1986, when I joined the flight simulation industry, I came across an internal report on quaternions, which were being used to control the rotational orientation of a simulated aircraft.

I can still remember being completely bemused by quaternions, simply because they involved so many imaginary terms. However, after much research I started to understand what they were, but not how they worked. Simultaneously, I was becoming interested in the philosophical side of mathematics, and trying to come to terms with the ‘real meaning’ of mathematics through the writing of Bertrand Russell. Consequently, concepts such as i were an intellectual challenge.

I am now comfortable with the idea that imaginary i is nothing more than a symbol, and in the context of algebra permits i2 =−1 to be defined. And I believe it is futile trying to discover any deeper meaning to its existence. Nevertheless, it is an amazing object within mathematics, and I often wonder whether there could be similar objects waiting to be invented.