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 September 19th, 2011, 06:03 AM #1 Member   Joined: Aug 2011 From: student Posts: 55 Thanks: 0 find the mistake ? We know that $\displaystyle i^{2} = -1$ and $\displaystyle i = \sqrt{-1}$ $\displaystyle i = \sqrt{-1} = \frac{\sqrt{-1}}{1} = \frac{\sqrt{-1}}{\sqrt{1}} = \sqrt{\frac{-1}{1}} = \frac{\sqrt{1}}{\sqrt{-1}} = \frac{1}{\sqrt{-1}} = \frac{1}{i}$ if the last expression $\displaystyle i = \frac{1}{i}$ both sides multiply with $\displaystyle i$ and find $\displaystyle i^{2} = 1$ $\displaystyle i^{2}=1$ ????? Last edited by skipjack; August 15th, 2019 at 04:54 AM. September 19th, 2011, 06:07 AM #2 Global Moderator   Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5 Re: find the mistake ? It's the middle "equality", when you say that the quotient of the radicals is the radical of quotients. September 19th, 2011, 04:02 PM #3 Global Moderator   Joined: May 2007 Posts: 6,849 Thanks: 742 Re: find the mistake ? √(-1) has two possibilities, i or -i, depending on the context. Last edited by skipjack; August 15th, 2019 at 05:02 AM. September 20th, 2011, 02:53 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,103 Thanks: 2321 That's confusing. There are two square roots of -1, namely i and -i, but √(-1) refers to i, not -i. The rule that √(a/b) = √a / √b does not apply when a is positive and b is negative. Use √(a/b) = - √a / √b instead. Similarly, the rule that √(a) √(b) = √(ab) is replaced with √(a) √(b) = - √(ab) if a and b are both negative. Last edited by skipjack; August 15th, 2019 at 05:01 AM. Tags find, mistake Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post dennisdixon Algebra 7 January 26th, 2013 08:19 AM livestrong136 Calculus 1 May 8th, 2012 05:02 AM r-soy Physics 4 March 2nd, 2012 01:17 AM bobar77 Algebra 8 February 17th, 2012 10:37 PM islam Calculus 6 December 3rd, 2010 08:33 PM

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