If \( z+z^{-1}=1 \) then the value of \( z^{100}+z^{-100} \) is....

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If \( z+z^{-1}=1 \) then the value of \( z^{100}+z^{-100} \) is
\( \mathrm{P} \)
(1) 1
(2) 2
(3) 0
(4) -1


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