WBJEE · Maths · Complex Number
If \(z_{1}\) and \(z_{2}\) be two non-zero complex numbers such that \(\frac{z_{1}}{z_{2}}+\frac{z_{2}}{z_{1}}=1,\) then the origin and the points represented by \(z_{1}\) and \(z_{2}\)
- A lie on a straight line
- B form a right angled triangle
- C form an equilateral triangle
- D form an is asceles triangle
Answer & Solution
Correct Answer
(C) form an equilateral triangle
Step-by-step Solution
Detailed explanation
We know that, if \(z_{1}, z_{2}\) and \(z_{3}\) are the vertices of an equilateral triangle. Then, \[ z_{1}^{2}+z_{2}^{2}+z_{3}^{2}-z_{1} z_{2}-z_{2} z_{3}-z_{3} z_{1}=0 \] Now, but we have…
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