Question

If A and B be two complex numbers satisfying $\frac{A}{B}+\frac{B}{A}=1$. Then the two points represented by A and B and the origin form the vertices of

• A. An equilateral triangle
• B. An isosceles triangle which is not equilateral
• C. An isosceles triangle which is not right angled
• D. A right angled triangle

Answer 1

The correct option is A An equilateral triangle

Given A and B are 2 complex numbers and $\frac{A}{B}+\frac{B}{A}-1$

Let $A=z_1$

$B=z_2$

$z_3=0$

$\frac{z_1}{z_2}+\frac{z_2}{z_1}=1\Rightarrow z_1^2+z_2^2=z_1{z}_2$

$\Rightarrow z_1^2+z_2^2+z_3^2=z_1{z}_2+z_2{z}_3+z_3{z}_1$

This means $z_1,z_2,z_3$ from an equilateral triangle