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Imaginary Numbers
Mathematicians did not welcome these new numbers overnight. It took a couple of centuries to develop a
consistent framework explaining how ?(-1) actually fitted into the rest of mathematics. The French mathematician Rene Descartes (1596 - 1650) derided these numbers, calling them imaginary (as opposed to
the useful, real numbers). But his name for them stuck. The square-root of minus one – whatever it was –
gained its own symbol. It was denoted in equations by the letter i, which made arithmetic with them less
cumbersome. No doubt it shielded nervous mathematicians from having to think too much about how
different ?(-1) was from the familiar, real numbers. The imaginary unit i was defined by the relationship
i^2=-1. In other words when you square this strange number, it takes a negative value.
Mathematicians noticed that when imaginary numbers cropped up in their calculations, they were often
bonded to real numbers. Written down they look like 3+4i or 2-5i. These mixtures of the real and imaginary are called a complex numbers.
Complex numbers are an amalgam of our familiar real numbers and the recently discovered imaginary.
ICY SCIENCE | WINTER 2013- 2014