A particle \( P \) starts from the point \( z_{0}=1+2 i, i=\sqrt{-1} \). It moves first horizontally away from origin by 5 units and
\( \mathrm{P} \) then vertically away from origin by 3 units to reach a
W point \( z_{1} \). From \( z_{1} \), the particle moves \( \sqrt{2} \) units in the direction of the vector \( \hat{\mathbf{i}}+\hat{\mathbf{j}} \) and then it moves through an angle \( \frac{\pi}{2} \) in anti-clockwise direction on a circle with centre at origin, to reach a point \( z_{2} \), then the point \( z_{2} \) is given by
[IIT-JEE 2008, 3M]
(a) \( 6+7 i \)
(b) \( -7+6 i \)
(c) \( 7+6 i \)
(d) \( -6+7 i \)
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