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by Kermit Author IconMail Icon
Rated: E · Essay · None · #2339906

Answered: Imaginary numbers aren't real, but aren't real numbers imaginary too?

Math questions
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?

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 nor greater than zero.

The real numbers were pictured as being on an infinitely long line. A point on that line was defined as the middle of the line and labeled as zero. Positive numbers were to the right of zero. Numbers were to the left of zero. were called negative. Adding a negative number is equivalent to subtracting the corresponding positive number.

Imaginary numbers could not be pictured 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 real and imaginary numbers.

In his book, "One, Two Three... Infinity," George Gamow discusses this representation of imaginary numbers and how to add imaginary numbers to real numbers to make complex numbers.

Another important point is that the square root of minus one is still one unit away from zero. It is one unit away in the vertical or "imaginary" direction.

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