My Math Forum Complex number help!

 Complex Analysis Complex Analysis Math Forum

 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:
 Originally Posted by razzatazz using the conjugate yes. but where to pull complex numbers from!
$\frac{1}{u}+ \frac{1}{v}= \frac{u+ v}{uv}$ for any numbers u and v. The "conjugate" has nothing to do with it.
So $\frac{1}{u}+ \frac{1}{v}= \frac{1}{uv}$ becomes $\frac{u+ v}{uv}= \frac{1}{uv}$ 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 $2vu+ u^2- 1= 0$ (you missed the "shift" key!). From u+ v= 1, above, v= 1- u so the equation becomes
$2(1- u)u+ u^2- 1$$= 2- 2u^2+ u^2- 1$$= 1- u^2= 0$. 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 2uv-u^2-1=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: 18,957 Thanks: 1604 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:
 Originally Posted by razzatazz Sorry, I hit the wrong button meant to be 2uv-u^2-1=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!
If, when you say "I solved for u= 1", you mean $1- u^2= 0$, u= 1 is one solutions but, since that is a quadratic equation, there is another solution.

 Tags complex, number

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Punch Complex Analysis 1 April 1st, 2012 09:01 AM panky Algebra 4 November 14th, 2011 10:15 PM gaussrelatz Algebra 7 October 18th, 2011 06:37 AM Number Theory 3 January 20th, 2011 05:15 AM TsAmE Complex Analysis 1 October 18th, 2010 04:38 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top