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Imaginary numbers.

Mathematicians knew that the multiplication of two negative numbers yields a positive product. Thus, not only does + 1 X + 1 = + 1, but - 1 X - 1 = + 1.

What number, then, multiplied by itself yields - 1? To put it another way, what is the square root of - 1? Mathematicians can invent the necessary number, call it an imaginary number, and symbolize it as i for imaginary. You can then say that + i X +i = -1.

What's more, -i X -i = -1.

Wallis (see 1668) succeeded in making sense out of such imaginary numbers in 1685.

Imagine a horizontal line. Mark off a point as zero and then imagine the positive numbers marked off to the right and the negative numbers marked off to the left, with all the fractions and irrational numbers appropriately marked off between the whole numbers. That is the real number axis.

Next, draw a vertical line passing through the zero point. Mark all the i numbers (i, 2i, 3i, and so on) upward, and all the -i numbers downward, with all the imaginary fractions and irrational numbers marked off, too. That is the imaginary number axis.

Every point in the plane can then be marked off just as Descartes did in his analytical geometry (see 1637). Every point (a) on the real number axis becomes a + 0i; every point (b) on the imaginary number axis becomes 0 + bi; and every number on neither axis (the complex numbers) becomes a + bi.

Such a scheme proved enormously useful to mathematicians, scientists, and engineers.

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Author:Asimov, Isaac
Publication:Asimov's Chronology of Science & Discovery, Updated ed.
Article Type:Reference Source
Date:Jan 1, 1994
Words:253
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