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To find the six complex sixth roots of unity and plot them.
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Answer to Problem 62AYU
The six complex roots of unity are
Explanation of Solution
1 can be written as the
Rewrite 1 in the form
The magnitude of 1,
The distinct complex roots of
are
, where
is a complex number,
and
The complex roots of are
Where
Substitute 0 for in
to get the first complex root of 1.
Substitute 1 for k in to get the second complex root of 1.
Substitute 2 for k in to get the third complex root of 1.
Substitute 3 for k in to get the fourth complex root of 1.
and
Therefore, the six complex roots of unity are
Plotting the six roots as follows-
Chapter 9 Solutions
Precalculus
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