A particle starts to travel from a point \( P \) on the curve \( C_{1} \) : \( |z-3-4 i|=5 \), w...

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A particle starts to travel from a point \( P \) on the curve \( C_{1} \) : \( |z-3-4 i|=5 \), where \( |z| \) is maximum. From \( P \), the particle moves through an angle \( \tan ^{-1} \frac{3}{4} \) in anticlockwise direction on \( |z-3-4 i|=5 \) and reaches at point \( Q \). From \( Q \), it comes down parallel to imaginary axis by 2 units and reaches at point \( R \). Find the complex number corresponding to point \( R \) in the Argand plane.
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