2022 AMC 12B Problems/Problem 11
Problem
Let , where
. What is
?
Solution
Converting both summands to exponential form,
Notice that both are scaled copies of the third roots of unity.
When we replace the summands with their exponential form, we get
When we substitute
, we get
We can rewrite
as
, how does that help?
Since any third root of unity must cube to
.
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