# How to plot complex eigenvalues of a matrix?

I have a matrix , for instance, like this :

matrix[a_ ] := {{0, a}, {-a, 1}};
Eigenvalues[matrix[a]]


and this give the eigenvalues that depends on a

{1/2 (1 - Sqrt[1 - 4 a^2]), 1/2 (1 + Sqrt[1 - 4 a^2])}

If I plot this eigenvalues,

Plot[Eigenvalues[mat[a, b, q]], {a, -1 , 2}]


this just give me the real value. I would like to have the real part of the complex number too. How can I get the real part of the complex eigenvalue?

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You can use ReIm or Re or Im:
mat[a_] := {{0, a}, {-a, 1}};