Complex Numbers And Quadratic Equations question 228
Question: The value of i1/3 is [UPSEAT 2002]
Options:
A) $ \frac{\sqrt{3}+i}{2} $
B) $ \frac{\sqrt{3}-i}{2} $
C) $ \frac{1+i\sqrt{3}}{2} $
D) $ \frac{1-i\sqrt{3}}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {i^{1/3}}={{( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} )}^{1/3}}=\cos \frac{\pi }{6}+i\sin \frac{\pi }{6} $ $ =\frac{\sqrt{3}}{2}+\frac{i}{2} $ .
BETA
