A particle P starts from the point $$z_0 = 1 + 2i$$, 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 center at origin, to reach a point $$z_2$$. The point $$z_2$$ is given by