Absolute Values and Imaginary Numbers
Date: 05/17/2000 at 08:44:11 From: Khaine Subject: Imaginary Numbers I see imaginary numbers as problems that cannot be solved. (The square root of a negative is impossible except with i.) So would this be an imaginary number also? |x|= -8 Since no absolute value can be negative, this, too, cannot be solved. Please answer. -Khaine
Date: 05/17/2000 at 12:55:44 From: Doctor Peterson Subject: Re: Imaginary Numbers Hi, Khaine. No, imaginary numbers aren't like magic keys that solve all unsolvable equations. They are defined very specifically, so that i is a number whose square is -1. From that definition, their properties can be proved - including the fact that they make sense, following all the normal rules for numbers. You can't just look at any equation with no solutions and say that its solution is "imaginary"; you would have to be able to say which imaginary (or complex) number it is, and you can't. The absolute value even of a complex number is still positive. You could try defining a new special number, say "f" for "fake," for which |f| = -1, so that |8f| = |8|*|f| = -8; but if you worked enough with that definition I think you would find that the "numbers" you had created didn't make any sense as numbers. It's an interesting thought, though; it might be worth while to go ahead and try that, and see what happens. See our Dr. Math FAQ on imaginary numbers: http://mathforum.org/dr.math/faq/faq.imag.num.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.