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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