If for \( z \) as real or complex, \( \left(1+z^{2}+z^{4}\right)^{8}=C_{0}+C_{1} z^{2}+C_{2} z^{...
If for \( z \) as real or complex, \( \left(1+z^{2}+z^{4}\right)^{8}=C_{0}+C_{1} z^{2}+C_{2} z^{4} \) \( +\cdots+C_{16} z^{32} \), then
(1) \( C_{0}-C_{1}+C_{2}-C_{3}+\cdots+C_{16}=1 \)
(2) \( C_{0}+C_{3}+C_{6}+C_{9}+C_{12}+C_{15}=3^{7} \)
(3) \( C_{2}+C_{5}+C_{8}+C_{11}+C_{14}=3^{6} \)
(4) \( C_{1}+C_{4}+C_{7}+C_{10}+C_{13}+C_{16}=3^{7} \)
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