equations with complex results

[chromos]

Other approach:

If you want find out if your system of equations has independent equations (or how many are dependent) then you can use rank of matrix (which is built in HP Prime too). In your example RANK(M1) is 2, so there are only two independent equations in your system of equations (I assume a31 = (-10+oi) is typo and it should be (-10+0i)).