Eigenvalues with complex roots?
Ok I’m trying to solve a 2×2 matrix for it’s eigenvalue. and the root I’m working is complex. This question is actually geared more toward complex numbers. In an example while creating my eigen basis I found myself with these two complex system of equations:
(2-2i)x -2 y = 0
4x – (2+2i)y = 0
So now the solution to this system of equations is :
(1-i)x – y =0
Pleaseee tell me why this is the solution! Like exactly what the reasoning is. I think it has to do with properties of complex numbers. Please help pleaseeee!
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assume x=a+ib and y=c+id, a b c d are reals.
Now put it in the two given equations and equate the real and imaginary parts. you will get 4 equations in a b c and d but these equations will be dependent on each other. solve for c and d in terms of a and b frm these equations and find the value of c+id=y….in terms of a abd b. u will get the required ans…:)
hope it helps
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