When England played Germany in the 1990 World Cup, everyone rushed to boil their kettles at half time, and the UK power network nearly went down as a result. In this video Chris Budd, mathematician and *Plus* author, explains how this kind of disaster can be prevented using complex numbers.

To find out more about this and other uses of complex numbers, see this collection of articles and videos. In particular, you might want to read *Complex electricity*.

Chris Budd OBE is Professor of Applied Mathematics at the University of Bath, Vice President of the Institute of Mathematics and its Applications, Chair of Mathematics for the Royal Institution, Gresham Professor of Geometry, and an honorary fellow of the British Science Association. He is particularly interested in applying mathematics to the real world and promoting the public understanding of mathematics.

He has co-written the popular mathematics book *Mathematics Galore!*, published by Oxford University Press, with C. Sangwin and features in the book *50 Visions of Mathematics* ed. Sam Parc.