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November 28th, 2012, 03:28 AM   #1
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Square root of minus one

How is this possible? Am I doing something wrong?
sqrt(-1) = (-1)^(1/2) = (-1)^(2/4) = 4th-root((-1)^2) = 4th-root(1) = 1
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November 28th, 2012, 03:55 AM   #2
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Re: Square root of minus one

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November 28th, 2012, 04:23 AM   #3
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Re: Square root of minus one

Here is a common error :



Another error :

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November 29th, 2012, 10:16 PM   #4
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Re: Square root of minus one

Quote:
Originally Posted by kustrle
How is this possible? Am I doing something wrong?
sqrt(-1) = (-1)^(1/2) = (-1)^(2/4) = 4th-root((-1)^2) = 4th-root(1) = 1
You won't get the wrong answer if you do the denominator first AND choose the appropriate 4th roots of minus 1 to square.







Squaring the other 2 4th roots of minus 1 produces -i

Why don't you try it?

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November 30th, 2012, 06:01 AM   #5
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Re: Square root of minus one

As with all numbers, -1 has two square roots. However, since the complex numbers do not form an "ordered" field, we cannot simply say "one is positive, the other negative". That is, we have to be very careful to distinguish between the two roots, else we run into the problems zaidalyafey notes.
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