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Let's say I want to multiply $(\frac{-1 - i \sqrt{3}}{2})(\frac{-1 + i \sqrt{3}}{2})$. Doing it by hand, we easily see that the answer is 1.

However, when I type

n(((-1 + sqrt(-3))/2)*((-1-sqrt(-3))/2))

in sage, I get

1 - 5.55111512312578 x 10^(-17)i

which is (of course) very close to 1...but its not exactly 1. Why is that? How do I fix this??