A particle $P$  starts from the point $z_0=1+2i,i=\sqrt{-1}$ . It moves first horizontally away from origin by 5 units  and 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 $\pi /2$  in anticlockwise direction on a circle with centre at origin, to reach a point $z_2$ , the point $z_2$  is given by :