Complex Numbers And Quadratic Equations question 347
Question: Let $ z_1 $ and $ z_2 $ be two complex numbers such that $ \frac{z_1}{z_2}+\frac{z_2}{z_1}=1 $ . Then
Options:
A) $ z_1,z_2 $ are collinear
B) $ z_1,z_2 $ and the origin form a right angled triangle
C) $ z_1,z_2 $ and the origin form an equilateral triangle
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ \frac{z_1}{z_2}+\frac{z_2}{z_1}=1\Rightarrow z_1^{2}+z_2^{2}=z_1z_2 $
Þ $ z_1^{2}+z_2^{2}+z_3^{2}=z_1z_2+z_1z_3+z_2z_3, $ where $ z_3=0 $
Þ $ z_1,z_2 $ and the origin $ (\because z_3=0) $ form an equilateral triangle.
BETA
