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MATH / The sets A={z:z¹⁸=1} and B={w:w⁴⁸=1} are both sets of complex roots of unity. The set C = {zw : z in A ~ mbox{and} ~ w in B} is also a set of complex roots of unity. How many disti…

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problem

The sets A={z:z18=1}A = \{z : z^{18} = 1\} and B={w:w48=1}B = \{w : w^{48} = 1\} are both sets of complex roots of unity. The set $C = \{zw : z \in A ~ \mbox{and} ~ w \in B\}$ is also a set of complex roots of unity. How many distinct elements are in CC^{}_{}?
Plain-text mathematical notation (without MathML)
The sets A={z:z¹⁸=1} and B={w:w⁴⁸=1} are both sets of complex roots of unity. The set $C = \{zw : z \in A ~ \mbox{and} ~ w \in B\}$ is also a set of complex roots of unity. How many distinct elements are in C_()^()?
Original LaTeX notation
The sets $A = \{z : z^{18} = 1\}$ and $B = \{w : w^{48} = 1\}$ are both sets of complex roots of unity. The set $C = \{zw : z \in A ~ \mbox{and} ~ w \in B\}$ is also a set of complex roots of unity. How many distinct elements are in $C^{}_{}$?

level

Level 4

type

Precalculus

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task_id
6a0b7c84-5fdf-5336-9032-b99425ac7669
task_key
precalculus--test--6a0b7c84-5fdf-5336-9032-b99425ac7669
task_revision_id
1
config / split
precalculus / test

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