My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 5th, 2013, 02:35 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.
razzatazz is offline  
 
March 5th, 2013, 02:42 AM   #2
Math Team
 
Joined: Apr 2010

Posts: 2,770
Thanks: 356

Re: Complex number help!

1/v +1/u = (u + v)/vu = 1/vu right?
Hoempa is offline  
March 5th, 2013, 03:48 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!
razzatazz is offline  
March 5th, 2013, 04:33 AM   #4
Math Team
 
Joined: Apr 2010

Posts: 2,770
Thanks: 356

Re: Complex number help!

conjugates?
(u + v)/vu = 1/vu gives u + v = 1 right (for uv <> 0).
In the second, eliminate v
Hoempa is offline  
March 5th, 2013, 08:17 AM   #5
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 5

Re: Complex number help!

Quote:
Originally Posted by razzatazz
using the conjugate yes.

but where to pull complex numbers from!
for any numbers u and v. The "conjugate" has nothing to do with it.
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!
HallsofIvy is offline  
March 5th, 2013, 03:23 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!
razzatazz is offline  
March 6th, 2013, 06:26 AM   #7
Global Moderator
 
Joined: Dec 2006

Posts: 16,919
Thanks: 1253

You need u + v = 1. Have you checked your working?
skipjack is offline  
March 12th, 2013, 11:50 AM   #8
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 5

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 , u= 1 is one solutions but, since that is a quadratic equation, there is another solution.
HallsofIvy is offline  
Reply

  My Math Forum > College Math Forum > Complex Analysis

Tags
complex, number



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Complex number. (Least value) Punch Complex Analysis 1 April 1st, 2012 09:01 AM
complex number panky Algebra 4 November 14th, 2011 11:15 PM
complex number gaussrelatz Algebra 7 October 18th, 2011 06:37 AM
complex number Number Theory 3 January 20th, 2011 06:15 AM
Finding real number in complex number TsAmE Complex Analysis 1 October 18th, 2010 04:38 PM





Copyright © 2017 My Math Forum. All rights reserved.