2. Calculate the value of the expression

$$
\left(\frac{-1+i \sqrt{3}}{2}\right)^{1986}+\left(\frac{-1-i \sqrt{3}}{2}\right)^{1986}
$$

i is the imaginary unit.
Solution. It is easily verified that

$$
\left(\frac{-1+i \sqrt{3}}{2}\right)^{3}=1=\left(\frac{-1-i \sqrt{3}}{2}\right)^{3}
$$

According to this, the given expression has a value of 2, since 3 is a divisor of 1986.