08 May 2009

We - ‘Hielo,

We - ‘Hielo,
Interesting factoid:

The square root of a positive integer may be rational or irrational, but is always real. The square root of a negative integer is always imaginary, and is plus-or-minus a real multiple of i. The square root of a multiple of i, however, can always be represented as a complex number — the sum of some real number and some imaginary number — and so can all other roots of all complex numbers. It can be said, then, that the complex numbers are as “complicated” as numbers can possibly be… at least, until we invent some new mathematical symbol to make it even worse.

The imaginary and complex numbers may seem like mathematical novelties with no real value whatsoever, but they do turn out to be useful in certain electrical engineering problems, as well as theoretical physics. (Tachyons, for instance, are particles that are supposed to travel faster than light, and therefore have imaginary mass.)


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