Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

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/   
    
Associated Topics:
High School Imaginary/Complex Numbers
High School Number Theory

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/