JEE Math Practice Question

Let $\theta_{1}, \theta_{2}, \ldots, \theta_{10}$ be positive valued angles (in radian) such that $\theta_{1}+\theta_{2}+\cdots+\theta_{10}=2 \pi$. Define the complex numbers $z_{1}=e^{i \theta_{1}}, z_{k}=z_{k-1} e^{i \theta_{k}}$ for $k=2,3, \ldots, 10$, where $i=\sqrt{-1}$. Consider the statements $P$ and $Q$ given below: \[ \begin{aligned} & P:\left|z_{2}-z_{1}\right|+\left|z_{3}-z_{2}\right|+\cdots+\left|z_{10}-z_{9}\right|+\left|z_{1}-z_{10}\right| \leq 2 \pi \\ & Q:\left|z_{2}^{2}-z_{1}^{2}\right|+\left|z_{3}^{2}-z_{2}^{2}\right|+\cdots+\left|z_{10}^{2}-z_{9}^{2}\right|+\left|z_{1}^{2}-z_{10}^{2}\right| \leq 4 \pi \end{aligned} \] Then,

1. A.$P$ is TRUE and $Q$ is FALSE
2. B.$Q$ is TRUE and $P$ is FALSE
3. C.both $P$ and $Q$ are TRUE
4. D.both $P$ and $Q$ are FALSE