A) \[cis\left( \frac{\pi }{2} \right)\]
B) \[cis\left( \frac{\pi }{12} \right)\]
C) \[cis\left( \frac{\pi }{6} \right)\]
D) \[cis\left( \frac{\pi }{3} \right)\]
Correct Answer: B
Solution :
\[\frac{1}{2}+i\frac{\sqrt{3}}{2}\]\[=\left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right)\] Now \[{{\left( \frac{1}{2}+i\frac{\sqrt{3}}{2} \right)}^{1/4}}={{\left( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} \right)}^{1/4}}\] \[=\left( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} \right)\]\[=cis\,\left( \frac{\pi }{12} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
