Let $z_k = \cos\left(\frac{2k\pi}{10}\right) + i\sin\left(\frac{2k\pi}{10}\right)$; $k = 1,2,\ldots,9$. List I P. For each $z_k$ there exists a $z_j$ such that $z_k \cdot z_j = 1$ Q. There exists a $k \in \{1,2,\ldots,9\}$ such that $z_1 \cdot z = z_k$ has no solution $z$ in the set of complex numbers. R. $\frac{|1-z_1||1-z_2|\cdots|1-z_9|}{10}$ equals S. $1 - \sum_{k=1}^{9} \cos\left(\frac{2k\pi}{10}\right)$ equals List II 1. True 2. False 3. 1 4. 2 P Q R S (A) 1243 (B) 2134 (C) 1234 (D) 2143
Let $z_k = \cos\left(\frac{2k\pi}{10}\right) + i\sin\left(\frac{2k\pi}{10}\right)$; $k = 1,2,\ldots,9$.
\textbf{List I}\\
P. For each $z_k$ there exists a $z_j$ such that $z_k \cdot z_j = 1$\\
Q. There exists a $k \in \{1,2,\ldots,9\}$ such that $z_1 \cdot z = z_k$ has no solution $z$ in the set of complex numbers.\\
R. $\frac{|1-z_1||1-z_2|\cdots|1-z_9|}{10}$ equals\\
S. $1 - \sum_{k=1}^{9} \cos\left(\frac{2k\pi}{10}\right)$ equals
\textbf{List II}\\
1. True\\
2. False\\
3. 1\\
4. 2
P Q R S\\
(A) 1243\\
(B) 2134\\
(C) 1234\\
(D) 2143