My Math Forum find the mistake ?

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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.

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