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There is a bizarre number in maths referred to simply as 鈥榠鈥�. It appears to break the rules of arithmetic - but turns out to be utterly essential for applications across engineering and physics. We鈥檙e talking about the square root of -1. WHICH MAKES NO SENSE.

Professor Fry waxes lyrical about the beauty and power of this so-called 鈥榠maginary鈥� number to a sceptical Dr Rutherford. Dr Michael Brooks tells the surprising story of the duelling Italian mathematicians who gave birth to this strange idea, and shares how Silicon Valley turned it into cold hard cash. It's all about oscillations, Professor Jeff O鈥機onnell demonstrates. And finally, Dr Eleanor Knox reveals that imaginary numbers are indispensable for the most fundamental physics of all: quantum mechanics.

Imaginary, impossible鈥�but essential!

Contributors: Professor Jeff O鈥機onnell, Ohlone College California, Dr Michael Brooks, Author of 'The Maths That Made Us', and Dr Eleanor Knox, Philosopher of Physics at KCL and a Senior Visiting Fellow at the University of Pittsburgh.

Producer: Ilan Goodman