# Question 5

Algebra Level 4

If $$A_{1}$$, $$A_{2}$$, $$A_{3}$$ are the arguments of the roots of the complex equation $$Z^3-\alpha^3=0$$, where $$\alpha$$ is a constant complex number with modulus $$1$$, find the value of: $\sum_{n=1}^{n=3}{\cos(A_{n})+\sin(A_{n})}$.

$$\bullet$$ This question is part of the set For the JEE-nius;P

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