If \( P \) is a point on the Aragand diagram. On the circle with \( O P \) as diameter two point...

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If \( P \) is a point on the Aragand diagram. On the circle with \( O P \) as diameter two points \( Q \) and \( R \) are taken such that \( \angle P O Q \) \( =\angle Q O R=\theta \). If \( O \) is the origin and \( P, Q \) and \( R \) are represented by the complex number \( Z_{1}, Z_{2} \) and \( Z_{3} \) respectively, show that : \( Z_{2}^{2} \cdot \cos 2 \theta=Z_{1} \cdot Z_{3} \cos ^{2} \theta \).
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