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 \(z_{2}\)

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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 \(z_{2}\)

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kritika · Answer 1 · 2021-12-27T07:05:54+0000

Ans: (C)
Hint \(: z_{1}{ }^{2}+z_{2}{ }^{2}+z_{2}{ }^{3}=z_{1} z_{2}+z_{2} z_{3}+z_{3} z_{1}\) is the condition for \(z_{1} z_{2} z_{3}\) to be the vertices of an equilateral triangle.
Putting \(z_{3}=0\)
\(z_{1}^{2}+z_{2}^{2}=z_{1} z_{2}\)

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 \(z_{2}\)

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