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The solutions are correct but they are not fully simplified.
sage: f= x^2 - (1 + I)*x + 6 + 3*I
sage: solve(f==0,x)
[x == -1/2*sqrt(-10*I - 24) + 1/2*I + 1/2, x == 1/2*sqrt(-10*I - 24) + 1/2*I + 1/2]
For each solution, you can simplify its right-hand-side as follows:
sage: [s.rhs().full_simplify() for s in solve(f==0,x)]
[3*I, -2*I + 1]
