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December 27th, 2014, 08:09 PM   #1
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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.
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