Complex Numbers And Quadratic Equations question 336
Question: Let $ z_1,z_2,z_3 $ be three vertices of an equilateral triangle circumscribing the circle $ |z| $ = $ \frac{1}{2} $ . If $ z_1=\frac{1}{2}+\frac{\sqrt{3}i}{2} $ and $ z_1,z_2,z_3 $ are in anticlockwise sense then $ z_2 $ is [Orissa JEE 2002]
Options:
A) $ 1+\sqrt{3}i $
B) $ 1-\sqrt{3}i $
C) 1
D) - 1 $ $
Show Answer
Answer:
Correct Answer: D
Solution:
$ z_2=z_1{e^{2i\pi /3}} $ $ =( \frac{1}{2}+\frac{\sqrt{3}}{2}i )( \cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3} ) $ $ =( \frac{1}{2}+\frac{\sqrt{3}}{2}i ) $ $ ( \frac{-1}{2}+\frac{\sqrt{3}}{2}i ) $ $ =-\frac{3}{4}-\frac{1}{4}=-1 $ .
BETA
