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An Imaginary Tale

Complex numbers are so widely used today that nobody really stops to think about where they were actually dervied from, and that they really have quite an interesting story behind them. Paul Nahin tells the story behind one of mathematics' most mysterious numbers - the square root of minus one, also known as 'i'. Nahin recreates the problems that were encountered while dealing with 'i' and describes the people who faced them, as well.

In 1878, two brothers stole some mathematical information from an ancient Egyptian burial site in the Valley of Kings, and thereby introduced scholars to the earliest known form of a square root of a negative number. In the first century, a mathematician-engineer Heron of Alexandria came across 'i' in a different project but faked the math behind it. Medieval mathematicians stumbled upon the number while studyin gnegative numbers, but dismissed it as a redundant error. Later on, at the time of Descartes, the use of negaive square root numbers was suspected,  but efforst to solve related problems led to bitter conflicts. The troublesome 'i' was finally categorised as a complex number to be further analysed in Napoleonic times.

Writing at a level that is suited to people with differnt kinds of mathematical backgrounds, Nahin adds interesting facts into his discussions, including the application of complex numbers to important problems, such as Kepler's laws of planetary motion and AC electrical circuits.