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 Complex Analysis Complex Analysis Math Forum

 December 27th, 2014, 08:09 PM #1 Newbie   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. Tags equivalence, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ChristinaScience Algebra 1 January 25th, 2014 06:33 PM Frenchie. Applied Math 4 January 24th, 2012 09:12 AM julian21 Algebra 3 December 8th, 2011 01:20 PM Nick1978 Applied Math 2 December 16th, 2010 08:21 AM Frenchie. Number Theory 3 December 31st, 1969 04:00 PM

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