Q. Consider the following statements : The points having affixes $\mathcal{z}_{1},\ \mathcal{z}_{2},\ \mathcal{z}_{3}$ from an equilateral triangle, iff $\frac{1}{\mathcal{z}_{1} - \mathcal{z}_{2}} + \frac{1}{\mathcal{z}_{2} - \mathcal{z}_{3}} + \frac{1}{\mathcal{z}_{3} - \mathcal{z}_{1}} = 0$ If $\mathcal{z}$ is a complex number, then $e^{\mathcal{z}}$ is periodic. If |$\ \mathcal{z}_{1}| = \left| \mathcal{z}_{2} \right|\ and\arg{\left( \frac{\mathcal{z}_{1}}{\mathcal{z}_{2}} \right) = \pi,\ then\ \mathcal{z}_{1} + \mathcal{z}_{2} = 0.}$ Which of the statements given above are correct?
A) (1)and (2)
B) (2)and (3)
C) (3)and (1)
D) All (1), (2) and (3)
Explanation
The correct answer is Option D: All (1), (2) and (3).
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.