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March 5th, 2013, 01:35 AM  #1 
Member Joined: Mar 2013 Posts: 56 Thanks: 0  Complex number help!
Hallo I have to find all complex numbers v and u satisfying 1/v +1/u = 1/vu AND 2vu = u^2 1 = 0 Please help! I don't know what to do. 
March 5th, 2013, 01:42 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: Complex number help!
1/v +1/u = (u + v)/vu = 1/vu right?

March 5th, 2013, 02:48 AM  #3 
Member Joined: Mar 2013 Posts: 56 Thanks: 0  Re: Complex number help!
using the conjugate yes. but where to pull complex numbers from! 
March 5th, 2013, 03:33 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: Complex number help!
conjugates? (u + v)/vu = 1/vu gives u + v = 1 right (for uv <> 0). In the second, eliminate v 
March 5th, 2013, 07:17 AM  #5  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Complex number help! Quote:
So becomes so u+ v= 1. Now what you wrote for your other equation, "2vu = u^2 1 = 0" is impossible. If 2vu= 0, then either u= 0 so 1/u is impossible, or v= 0 so 1/v= 0. I think what you intended was (you missed the "shift" key!). From u+ v= 1, above, v= 1 u so the equation becomes . Solve that equation for u, then find v. This involves "complex numbers" only in the sense that the set of complex numbers includes the real numbers and so integers!  
March 5th, 2013, 02:23 PM  #6 
Member Joined: Mar 2013 Posts: 56 Thanks: 0  Re: Complex number help!
Sorry, I hit the wrong button meant to be 2uvu^21=0 I solved for u = 1 and then with that, v = 1 as well. Is that right? Thank you so so so much for you help! 
March 6th, 2013, 05:26 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,037 Thanks: 1394 
You need u + v = 1. Have you checked your working?

March 12th, 2013, 11:50 AM  #8  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Complex number help! Quote:
 

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