If P and Q are respectively by the complex numbers z1 and z2 such that - 1 z 1 - 1 z 2 - - 1 z 1 - 1 z 2 - then the circumcentre of OPQ where O is the origin is

The correct option is B z_1+z_22 ...

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Byju's Answer

Standard VIII

Mathematics

Area of Polygons

If P and ...

Question

If $P$ and $Q$ are respectively by the complex numbers $z_{1}$ and $z_{2}$ such that $∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{1}{z_{1}} - \frac{1}{z_{2}} ∣ ∣ ∣$ , then the circumcentre of $△ O P Q$ (where $O$ is the origin) is

\frac{z_{1} - z_{2}}{2}

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\frac{z_{1} + z_{2}}{2}

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\frac{z_{1} - z_{2}}{3}

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z_{1} + z_{2}

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Solution

The correct option is B $\frac{z_{1} + z_{2}}{2}$

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If P and Q are represented by the numbers $z_{1}$ and $z_{2}$ such that $∣ ∣ ∣ \frac{1}{z_{2}} + \frac{1}{z_{1}} ∣ ∣ ∣$ = $∣ ∣ ∣ \frac{1}{z_{2}} - \frac{1}{z_{1}} ∣ ∣ ∣$ , then the circumcentre of $△ O P Q$ ,(where O is the origin) is