Years ago I participated in answering questions kids asked

about math.

One of the questions was:

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Imaginary numbers aren't real, but aren't real numbers

imaginary too?

Answered by Kermit Rose.

Yes. All numbers are in our imagination. So in that sense

"real" numbers are just as imaginary as "imaginary" numbers.

The term imaginary was applied when it was noticed that these

numbers are neither less than or greater than zero.

The real numbers were pictured as being on an infinitely long

line. A point on that line was thought as the middle of the

line, and labeled as zero. Positive numbers were to the right

of zero. Negative numbers were to the left of zero.

Imaginary numbers could not be pictured as on the line at

all.

Since nobody knew, at the time, how to picture imaginary

numbers, it made sense to call them imaginary.

Later it was figured out that we could picture the imaginary

numbers by placing them on a line perpendicular to the real

number line. Another infinitely long line perpendicular to

the real number line goes through the zero point. So zero

is the zero for both real numbers and for imaginary numbers.

George Gamow's book, "One, Two Three . . . Infinity" talks

a little bit about this representation of imaginary numbers

and also talks about adding imaginary numbers to real numbers

to make complex numbers.

Another important point is that the square root of -1 is

still one unit away from zero. It is just that it is one

unit away in the vertical or "imaginary" direction.

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