Find roots of
-\lambda ^3 +(2+2i)\lambda^2-3i\lambda-(1-i) = 0
The Attempt at a Solution
I tried my old trick
I tried to separating the 4 terms into 2 pairs and try to find a common factor in the form of ##\lambda + z## between them,
-\lambda ^2 (\lambda -2-2i) - 3i\lambda -1+i
It doesn't seem to work.
-\lambda (\lambda^2 +3i) - (2+2i)\lambda -1+i
And I am out of tricks.
Should I keep trying to factorize it or there is something else I should do about polynomial with complex coefficient?