Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.
All the numbers on the number line, when squared, yield a positive number; 22 = 4, and (-2)2 = 4. Mathematicians started calling those familiar numbers “real” and the apparently impossible breed of numbers “imaginary.”
Imaginary numbers, labeled with units of i (where, for instance, (2i)2 = -4), gradually became fixtures in the abstract realm of mathematics. For physicists, however, real numbers sufficed to quantify reality. Sometimes, so-called complex numbers, with both real and imaginary parts, such as 2 + 3i, have streamlined calculations, but in apparently optional ways. No instrument has ever returned a reading with an i.
Yet physicists may have just shown for the first time that imaginary numbers are, in a sense, real.
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