Find all $z$ such that $$z^3 + (i-1)z^2 - iz = 0$$
$$z = (1-i)/2 + \sqrt{(i-1)^2 +4i}/2$$ $$ z= (1-i)/2 + \sqrt{2i}/2$$
I'm not sure where to go from this since we have a square root of a complex number. What's the next step?
2026-03-27 12:28:45.1774614525
Find all solutions to $ z$ using the quadratic formula
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Alt. hint: $z^3 + (i-1)z^2 - iz = z(z^2-z + i z - i)=z\big(z(z-1)+i(z-1)\big)=\ldots$