A particle $P$ starts from the point $z _ { 0 } = 1 + 2 i$, where $i = \sqrt { - 1 }$. It moves first horizontally away from 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 (A) $6 + 7 i$ (B) $- 7 + 6 i$ (C) $7 + 6 i$ (D) $- 6 + 7 i$
A particle $P$ starts from the point $z _ { 0 } = 1 + 2 i$, where $i = \sqrt { - 1 }$. It moves first horizontally away from 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\\
(A) $6 + 7 i$\\
(B) $- 7 + 6 i$\\
(C) $7 + 6 i$\\
(D) $- 6 + 7 i$