Roots of the polynomial x^4-(1+2i)*x^2+2i

Unpolished roots:
        root #          real         imag.
          1          -1.000000    -1.000000
          2          -1.000000     0.000000
          3           1.000000     1.000000
          4           1.000000     0.000000

Corrupted roots:
        root #          real         imag.
          1          -1.010000    -1.010000
          2          -1.020000     0.000000
          3           1.030000     1.030000
          4           1.040000     0.000000

Polished roots:
        root #          real         imag.
          1          -1.000000    -1.000000 
          2          -1.000000     0.000000 
          3           1.000000     1.000000 
          4           1.000000     0.000000