If $a=\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}$, then the value of $\left(\frac{1+a}{2}\right)^{3

Question

If $a=\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}$, then the value of $\left(\frac{1+a}{2}\right)^{3 n}$ is

Professor PC Thomas Classes · Answer

Use properties of cube roots of unity.