Question

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

• A. $-1$
• B. 1
• C. $3/2$
• D. $-1/2$

Answer 1

Answer: (B)

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