Complex Numbers And Quadratic Equations question 282
Question: If $ z=\frac{\sqrt{3}+i}{-2} $ , then $ z^{69} $ is equal to [RPET 2001]
Options:
A) 1
B) - 1
C) i
D) - i
Show Answer
Answer:
Correct Answer: C
Solution:
$ z=\frac{\sqrt{3}+i}{-2} $
$ \Rightarrow $ $ iz=-\frac{-1+\sqrt{3i}}{2}=-\omega $
$ \Rightarrow $ $ z=\frac{-\omega }{i}=i\omega $
$ \Rightarrow $ $ z^{69}=i^{69}.{{\omega }^{69}}=i $ $ (\because {{\omega }^{3n}}=i^{4n}=1) $
BETA
