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Imaginary Number Manipulations

Date: 7/10/96 at 18:59:48
From: Anonymous
Subject: Imaginary Number Manipulations

Hi, Dr. Math!

I have recently been doing some manipulations with the imaginary 
number (i), and in some of them negative (i) seems to "turn into" 
positive (i).  Consider the situation below:

                                1.5       3/2                   3
-i = -1 x square root(-1) = (-1)    = (-1)    = square root((-1) ) = 
square root(-1) = i

For some reason, a factor of -1 disappears, resulting in the seemingly 
absurd equation -i = i.  I have tried to find a mistake in the above, 
but found none (unless some fundamental rules are different for 
imaginary numbers).  I am also wondering if there is a rule that 
states that (i) cannot be renamed as the square root of -1, although 
the two are (supposed to be) equal.  Do you know what is going on 

Artem Gleyzer

Date: 7/10/96 at 20:39:42
From: Doctor Anthony
Subject: Re: Imaginary Number Manipulations

The square root of (-1) is +or- i

consider (+i)*(+i) = i^2 = -1

and      (-i)*(-i) = i^2 = -1

When you take square roots in an equation, you will in general have to 
consider that one of your 'solutions' may be wrong.

One relationship worth remembering is that  1/i = -i

-Doctor Anthony,  The Math Forum
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Associated Topics:
High School Imaginary/Complex Numbers

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