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
December 27th, 2014, 08:09 PM   #1
Newbie
 
kelsiu's Avatar
 
Joined: Jun 2014
From: Hong Kong

Posts: 7
Thanks: 0

Problem about equivalence

Suppose we have two equation x1=Ae^iωt + Be^-iωt and x2=A*e^-iωt + B*e^iωt . Where A and B are complex number and A* B* are their conjugate correspondingly.

Now if we want to make x1 and x2 exactly equivalent all the time, one way to do it is to have A=B* and B=A* so that x1 and x2 are equivalent. However, if we don't do it by this approach but instead set (A-B*)e^iωt=(A*-B)e^-iωt, then we have e^i2ωt=(A*-B)/(A-B*). I would like to ask if the A and B chosen can satisfy this criteria (even A≠B* and B≠A*), can we still say that x1 ≡ x2 ?

Another thing trouble me is if A=B* and B=A* , then e^i2ωt=(A*-B)/(A-B*)=0/0 which is undefined. What causes this problem?

Last edited by kelsiu; December 27th, 2014 at 08:12 PM.
kelsiu is offline  
 
Reply

  My Math Forum > College Math Forum > Complex Analysis

Tags
equivalence, problem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Equivalence ChristinaScience Algebra 1 January 25th, 2014 06:33 PM
Logical Equivalence problem Frenchie. Applied Math 4 January 24th, 2012 09:12 AM
Equivalence julian21 Algebra 3 December 8th, 2011 01:20 PM
Logical Implication and Equivalence Problem Nick1978 Applied Math 2 December 16th, 2010 08:21 AM
Logical Equivalence problem Frenchie. Number Theory 3 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.