
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 1st, 2012, 03:36 AM  #1 
Newbie Joined: Sep 2012 Posts: 11 Thanks: 0  How to prove that "i(ioota)" is irrational?
How to prove that "i(ioota)" is irrational by means of contradiction method?

September 1st, 2012, 03:39 AM  #2  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to prove that "i(ioota)" is irrational? Quote:
 
September 1st, 2012, 03:46 AM  #3 
Newbie Joined: Sep 2012 Posts: 11 Thanks: 0  Re: How to prove that "i(ioota)" is irrational?
?1 or sqrt(1)

September 1st, 2012, 03:49 AM  #4 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to prove that "i(ioota)" is irrational?
Oh, you're talking about imaginary unit then. But, i is neither rational nor irrational. In some sense, it can be even called rational since the absolute value of i is 1, which is rational. But i is never irrational. 
September 1st, 2012, 03:53 AM  #5 
Newbie Joined: Sep 2012 Posts: 11 Thanks: 0  Re: How to prove that "i(ioota)" is irrational?
but i need to prove it as irrational by using contradiction method.

September 1st, 2012, 03:55 AM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to prove that "i(ioota)" is irrational? Quote:
i is neither rational nor irrational I told you that. From where did you got this problem?  
September 1st, 2012, 04:03 AM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,163 Thanks: 472 Math Focus: Calculus/ODEs  Re: How to prove that "i(ioota)" is irrational?
I suppose you could begin be assuming i is rational: where Since we must have and , we have a contradiction. 
September 1st, 2012, 04:05 AM  #8  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to prove that "i(ioota)" is irrational? Quote:
 
September 1st, 2012, 04:08 AM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,163 Thanks: 472 Math Focus: Calculus/ODEs  Re: How to prove that "i(ioota)" is irrational?
Well, we have really only shown that i is not real, but as it's not real, then it's also not rational! 
September 1st, 2012, 04:10 AM  #10  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to prove that "i(ioota)" is irrational? Quote:
 

Tags 
iioota, irrational, prove 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A really hard math problem "Prove that if..."  isel  Algebra  8  September 22nd, 2013 09:35 AM 
A "simple" application of dirac delta "shift theorem"...help  SedaKhold  Calculus  0  February 13th, 2012 11:45 AM 
"separate and integrate" or "Orangutang method"  The Chaz  Calculus  1  August 5th, 2011 09:03 PM 
sample exerimentneed help finding "statistic" and "result"  katie0127  Advanced Statistics  0  December 3rd, 2008 01:54 PM 
How to prove that "i(ioota)" is irrational?  muhammadmasood  Abstract Algebra  6  December 31st, 1969 04:00 PM 