Let \( \theta_{1}, \theta_{2}, \ldots, \theta_{10} \) be positive valued angles (in radian) such that \( \theta_{1}+\the…

Let \( \theta_{1}, \theta_{2}, \ldots, \theta_{10} \) be positive valued angles (in radian) such that \( \theta_{1}+\theta_{2}+\ldots+\theta_{10}=2 \pi \). 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:

\(\begin{array}{l}P:\left|z_{2}-z_{1}\right|+\left|z_{3}-z_{2}\right|+\ldots+\left|z_{10}-z_{9}\right|+\left|z_{1}-z_{10}\right| \leq 2 \pi \\Q:\left|z_{2}^{2}-z_{1}^{2}\right|+\left|z_{3}^{2}-z_{2}^{2}\right|+\ldots+\left|z_{10}^{2}-z_{9}^{2}\right|+\left|z_{1}^{2}-z_{10}^{2}\right| \leq 4 \pi\end{array}\)

.Then,

[JEE Advanced 2021]