Complex Numbers And Quadratic Equations question 289
Question: . Which of the following is a fourth root of $ \frac{1}{2}+\frac{i\sqrt{3}}{2} $ [Karnataka CET 2003]
Options:
A) $ cis( \frac{\pi }{2} ) $
B) $ cis( \frac{\pi }{12} ) $
C) $ cis( \frac{\pi }{6} ) $
D) $ cis( \frac{\pi }{3} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{1}{2}+i\frac{\sqrt{3}}{2} $ $ =( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} ) $ Now $ {{( \frac{1}{2}+i\frac{\sqrt{3}}{2} )}^{1/4}}={{( \cos \frac{\pi }{3}+i\sin \frac{\pi }{3} )}^{1/4}} $ $ =( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} ) $ $ =cis( \frac{\pi }{12} ) $ .
BETA
