kill(all)$

van=facebook.com/LearningCalculus$

f(z):=z^3 -3*z^2 + 3*z - sqrt(3)*%i;

realpart(f(z));

imagpart(f(z));

solutions:solve(f(z),z)$

a:rectform(first(solutions))$[trigsimp(realpart(rhs(a))),trigsimp(imagpart(rhs(a)))];

b:rectform(second(solutions))$[trigsimp(realpart(rhs(b))),trigsimp(imagpart(rhs(b)))];

c:rectform(third(solutions))$[trigsimp(realpart(rhs(c))),trigsimp(imagpart(rhs(c)))];