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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 (AB*)e^iωt=(A*B)e^iωt, then we have e^i2ωt=(A*B)/(AB*). 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)/(AB*)=0/0 which is undefined. What causes this problem? Last edited by kelsiu; December 27th, 2014 at 08:12 PM. 

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