Matlab code

A = [ 2 i 4-2i ; -i 2 -i ; 4+2i i -1 ]

A =

   2.0000 + 0.0000i   0.0000 + 1.0000i   4.0000 - 2.0000i
   0.0000 - 1.0000i   2.0000 + 0.0000i   0.0000 - 1.0000i
   4.0000 + 2.0000i   0.0000 + 1.0000i  -1.0000 + 0.0000i

>> e = eig(A)

e =

   -4.2421
    1.5258
    5.7163

>> format rat
>> e = eig(A)

e =

   -1752/413
    1123/736
     806/141