Trigonometry Has Come Back

Algebra Level 5

The sets \( A = \big\{ z : z^{18} = 1 \big\} \) and \( B = \big\{ w : w^{48} = 1 \big\} \) are both sets of complex roots of unity. If we define \( C = \big\{ z \cdot w : z \in A, w \in B \big\} \), another set of complex roots of unity, find the amount of elements in \( C \).

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