Question A particle \( P \) starts from the point \( z_{0}=1+2 i \), where \( i=\sqrt{-1} \). It....

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A particle \( P \) starts from the point \( z_{0}=1+2 i \), where \( i=\sqrt{-1} \). It moves first horizontally away origin by 5 units and then vertically away from origin by 3 units to reach a point \( z_{1} \). From \( z_{1} \) the particle moves \( \sqrt{2} \) units in the direction of the vector \( \hat{i}+\hat{j} \) and then it moves through an angle \( \frac{\pi}{2} \) in anticlockwise direction on a circle with centre at origin to reach a point \( z_{2} \). The point \( z_{2} \) is given by
(1) \( 6+7 i \)
(2) \( -7+6 i \)
(3) \( 7+6 i \)
(4) \( -6+7 i \)


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