Phrases Previous Year Questions (PYQs) – Complex Number

If $x_k=\cos (\frac{2\pi k}{n})+i\sin (\frac{2\pi k}{n})$ , then $\sum _{k=1}^n(x_k)=?$

A particle P starts from the point z₀=1+2i, where i=√−1 . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z₁. From z₁ the particle moves √2 units in the direction of the vector $\hat{i}+\hat{j}$ and then it moves through an angle ${\displaystyle \frac{\pi }{2}}$ in anticlockwise direction on a circle with centre at origin, to reach a point z₂. The point z₂ is given by