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
P numbers \( z_{1}=e^{i \theta_{1}}, z_{k}=z_{k-1} e^{i \theta_{k}} \) for \( k=2,3, \ldots, 10 \),
W 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]
(a) Pis TRUE and Q is FALSE
(b) Q is TRUE and P is FALSE
(c) both P and Q are TRUE
(d) both P and Q are FALSE
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