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Byju's Answer
Standard XIII
Mathematics
Cube Root of a Complex Number
If z=-2+2√3 i...
Question
If
z
=
−
2
+
2
√
3
i
,
then
z
2
n
+
2
2
n
z
n
+
2
4
n
may be equal to
A
3
⋅
4
2
n
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B
2
2
n
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C
2
⋅
4
2
n
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D
0
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Solution
The correct option is
D
0
ω
=
−
1
+
√
3
i
2
z
=
−
2
+
2
√
3
i
=
4
ω
∴
z
2
n
+
2
2
n
z
n
+
2
4
n
=
(
4
ω
)
2
n
+
2
2
n
(
4
ω
)
n
+
2
4
n
=
4
2
n
⋅
ω
2
n
+
2
2
n
⋅
4
n
⋅
ω
n
+
2
4
n
=
4
2
n
[
ω
2
n
+
ω
n
+
1
]
=
{
0
, if
n
is not a multiple of
3
3
⋅
4
2
n
, if
n
is a multiple of
3
Suggest Corrections
0
Similar questions
Q.
If
z
=
−
2
+
2
√
3
i
,
then
z
2
n
+
2
2
n
z
n
+
2
4
n
may be equal to
Q.
If
z
=
−
2
+
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√
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n
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lf
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1
+
i
√
3
and
n
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3
,
then
Z
2
n
+
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n
Z
n
+
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is equal to
Q.
If
z
=
cos
θ
+
i
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, then
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Q.
If
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/
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=
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c
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Then prove that
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−
1
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/
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=
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t
a
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θ
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Cube Root of a Complex Number
Standard XIII Mathematics
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