Q. For three complex numbers $1 - i,\ i,\ 1 + i$ which of the following is true?
A) They form a right triangle
B) They are collinear
C) They form an equilateral triangle
D) They form an isosceles triangle
Explanation
(d)
Let $z_{1} = 1 - i,\ \ \ z_{2} = i$ and $z_{3} = 1 + i$
$\therefore\ \ \ \ \ \left| z_{1} \right| = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$
$\left| z_{2} \right| = \sqrt{1^{2}} = 1$
And $\left| z_{3} \right| = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$
Hence, given complex numbers form an isosceles triangle.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.