Complex Numbers And Quadratic Equations question 260
Question: The $ n^{th} $ roots of unity are in [Orissa JEE 2004]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ x^{n}=1=(\cos 0+i\sin 0^{o})=\cos 2r\pi +i\sin 2r\pi ={e^{i2r\pi }} $
Þ $ x={e^{i(2r\pi /n)}},r=0,1,2 $ ?……. Obviously the roots are $ 1,{e^{2\pi i/n}},{e^{4\pi i/n}} $ …… which are obviously in G.P. with common ratio $ {e^{2\pi i/n}} $ .
BETA
