Imaginary Number ManipulationsDate: 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 here? 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 Check out our web site! http://mathforum.org/dr.math/ |
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