Match List-I with List-II:
\[
\begin{array}{|l|l|}
\hline
\textbf{List-I (Equation)} & \textbf{List-II (Roots)} \\
\hline
(A)\; (z + 1)^{2n} + (z - 1)^{2n} = 0 & (I)\; \cos\!\left(\tfrac{\pi}{5}\right) \pm i\sin\!\left(\tfrac{\pi}{5}\right), -1, \cos\!\left(\tfrac{3\pi}{5}\right) \pm i\sin\!\left(\tfrac{3\pi}{5}\right) \\
\hline
(B)\; z^5 + z^4 + z^3 + z^2 + z + 1 = 0 & (II)\; \text{purely imaginary number} \\
\hline
(C)\; (z-1)^5 + z^5 = 0 & (III)\; -1,\; \pm\frac{1}{2} \pm i\frac{\sqrt{3}}{2} \\
\hline
(D)\; z^5 + 1 = 0 & (IV)\; \tfrac{1}{2}\left[1+i\cot\!\left(\tfrac{p\pi}{10}\right)\right], \; p = 1,3,5,7,9 \\
\hline
\end{array}
\]
Choose the correct answer from the options given below: