<s>[INST] Solving $(1-x)^3 = -1$ over the complex field 
What are the solutions of: $(1-x)^3 = -1$ over $\mathbb{C}$?

We have one real solution which is $2$ so there are two complex solutions. 
 [/INST] Using the fact that $a^3 + 1 = (a+1)(a^2 - a +1)$, we have $$(1-x)^3 + 1 = 0 \iff \Big((1-x)+1\Big)\Big((1-x)^2 - (1-x) + 1\Big) = (2 - x)(x^2 - x + 1)\\ \implies x = 2\, \text{ or }\, x^2 - x + 1 = 0$$
Use the quadratic formula on the remaining quadratic to solve for the remaining two roots.
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