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  4. The product of all the roots of ( cos (π/3)+i sin (π/3))3 / 4 is

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Q. The product of all the roots of $\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)^{3 / 4}$ is

Complex Numbers and Quadratic Equations

Solution:

Product of roots of $\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)^{3 / 4}$
$=(-1)^3(\cos \pi+i \sin \pi)=1$