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November 28th, 2012, 03:28 AM  #1 
Newbie Joined: Dec 2010 Posts: 8 Thanks: 0  Square root of minus one
How is this possible? Am I doing something wrong? sqrt(1) = (1)^(1/2) = (1)^(2/4) = 4throot((1)^2) = 4throot(1) = 1 
November 28th, 2012, 03:55 AM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Square root of minus one 
November 28th, 2012, 04:23 AM  #3 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Square root of minus one
Here is a common error : Another error : 
November 29th, 2012, 10:16 PM  #4  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Square root of minus one Quote:
Squaring the other 2 4th roots of minus 1 produces i Why don't you try it?  
November 30th, 2012, 06:01 AM  #5 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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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