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Byju's Answer
Standard XII
Mathematics
Cube Root of a Complex Number
If ω is a c...
Question
If
ω
is a complex cube root of unity, then
sin
ω
10
+
ω
23
π
−
π
4
is equal to
A
1
√
2
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B
1
2
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C
1
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D
√
3
2
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Solution
The correct option is
A
1
√
2
Since,
ω
is a cube root of unity,
∴
sin
ω
10
+
ω
23
π
−
π
4
=
sin
ω
+
ω
2
π
−
π
4
=
sin
−
π
−
π
4
(
∵
1
+
ω
+
ω
2
=
0
)
=
sin
−
π
−
π
4
=
sin
π
4
=
1
√
2
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