If \( z=\left|a+b \omega+c \omega^{2}\right| \), where \( \omega \) is a cube root of unity and ...

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If \( z=\left|a+b \omega+c \omega^{2}\right| \), where \( \omega \) is a cube root of unity and \( a, b, c \in\{1,2,3, \ldots 10\} \), then the number of ordered triplets \( (a, b, c) \) for which \( z=1 \) is
(A) 18
(B) 10
(C) 30
(D) none of these
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