Complex Numbers And Quadratic Equations question 463
Question: If $ z_1 $ , $ z_2 $ , $ z_3 $ are the vertices of an equilateral triangle ABC such that $ | z_1-i | $ = $ | z_2-i | $ = $ | z_3-i | $ ,then $ | z_1+z_2+z_3 | $ equals to
Options:
A) $ 3\sqrt{3} $
B) $ \sqrt{3} $
C) 3
D) $ \frac{1}{3\sqrt{3}} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Given that. $ | z_1-i |=| z_2-i |=| z_3-i | $ Hence, $ z_1 $ , $ z_2 $ , $ z_3 $ , lie on the circle whose center is i. Also cirucmcenter coincides.
$ \therefore \frac{z_1+z_2+z_3}{3}=i $
$ \Rightarrow | z_1+z_2+z_3 |=3 $
BETA
