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## Homework Statement

R' = aJ

J' = bR

What happens to the graphs of R(t) and J(t)?

## The Attempt at a Solution

I made the matrix {{0, a}{b, 0}} and then got the equation (L=lambda) L^2 - 0L + (a+b) after computing the trace and determinant of that matrix. I then solved for the eigenvalues using the quadratic and got L1 = i sqrt(a+b) and L2 = -i sqrt(a+b)

But I didn't think I was supposed to get imaginary numbers when dealing with eigenvalues because then I can't graph the eigenvectors on the real plane. Did I do something wrong?

Thanks.