Question: Why does LinearAlgebra:-Eigenvectors(A) give a relatively complicated answer for a relatively simple 2x2 matrix A?

Consider the task of finding the eigenvalues and eigenvectors of a simple 2x2 matrix.

Usually I can insert the contents of a Maple worksheet here, but for some reason the following worksheet cannot be inserted:

In that worksheet I try to use LinearAlgebra:-Eigenvectors(A). The eigenvalues contain a complex term, even though they are real for the given matrix. It's not clear what criteria are used in selecting a specific eigenvector for each eigenvalue.

I then show a more manual calculation.

I was expecting to obtain a simpler solution to this problem using LinearAlgebra:-Eigenvectors(A). Is this expectation unjustified? I am asking primarily from the perspective of a user of the software. 

It would be interesting to know the answer from the perspective of someone who knows the ins and outs of the implementation of the software as well, but as a user my initial expectation is a more digestible result that doesn't rely on knowing such implementation details.

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