Compute $e^{{-2\pi i}/3}$ in GAP.

Question

I tried to calculate the following expression in GAP, but failed:

gap> E(-3);
Error, E: <n> must be a positive small integer (not the integer -3)
not in any function at *stdin*:49
type 'quit;' to quit to outer loop

So, how can I compute the expression like exp(2πi/-3) in GAP?

EDIT: Thank you, MathGeek, I figured out the following expression based on your clues:

gap> Cos(-2* FLOAT.PI/3);
-0.5
gap> Sin(-2* FLOAT.PI/3);
-0.866025

So, $e^{{2\pi i}/3}$ should be expressed as follows:

gap> [Cos(-2* FLOAT.PI/3), Sin(-2* FLOAT.PI/3)];
[ -0.5, -0.866025 ]

Regards, HZ

Answer 1

We can use Euler's formula for this. $$e^{ix}= cos(x)+isin(x)$$ We can input ${-2\pi}/3$ for $x$ to get the following: $$e^{{-2\pi i}/3}= cos({-2\pi}/3)+isin({-2\pi}/3)$$ Hopefully these inputs are valid in GAP.