Let z=((√ 3)/2+i/2)^5+((√ 3)/2-i/2)^5. If R (z) and I (z) respectively denote the real and imaginary parts of z, then:

Let $\displaystyle z=\left(\frac{\sqrt{3}}{2}+\frac{\mathrm{i}}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{\mathrm{i}}{2}\right)^5$. If $\displaystyle \mathrm{R}(z)$ and $\displaystyle \mathrm{I}(z)$ respectively denote the real and imaginary parts of $\displaystyle z$, then :