Question

Let A,B,C are 3 points on the complex plane represented by complex numbers a,b,c respectively such that |a| = |b| = |c| =1, a+b+c=1 and abc=1,then

• A. area of triangle ABC is 2 (Sq.unit)
• B. $△ABC$ is an equilateral triangle.
• C. $△ABC$ is right isosceles triangle.
• D. orthocentre of $△ABC$ lies outside the triangle.

Answer 1

The correct option is C $△ABC$ is right isosceles triangle.

$\overline{a}+\overline{b}+\overline{c}=1$



$\Rightarrow ab+bc+ca=1$

$\Rightarrow$ a,b,c are roots of cubic

$z^3-z^2+z-1=0$

$\Rightarrow (z^2+1)(z-1)=0$

$Z=\pm i,1$