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Byju's Answer
Standard XII
Mathematics
Properties of Modulus
Let z=√3-i/...
Question
Let
z
=
√
3
−
i
2
then
(
z
107
+
i
107
)
25
is equal to
A
z
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B
z
2
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C
z
3
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D
z
4
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Solution
The correct option is
A
z
Given
z
=
√
3
−
i
2
=
i
−
i
2
√
3
2
⇒
z
=
i
(
−
1
−
i
√
3
2
)
=
i
ω
2
=
(
i
ω
)
∴
z
107
=
i
107
ω
214
=
−
i
ω
and
∴
i
107
=
−
i
∴
z
107
+
i
107
=
−
i
ω
−
i
=
−
i
(
1
+
ω
)
=
i
ω
2
∴
(
z
107
+
i
107
)
25
=
(
i
ω
2
)
25
=
i
25
ω
50
=
i
ω
2
=
z
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Similar questions
Q.
If
z
1
,
z
2
,
z
3
are the solutions of
z
2
+
¯
¯
¯
z
=
z
,
then
z
1
+
z
2
+
z
3
is equal to
(
z
is a complex number on the Argand plane and
i
=
√
−
1
)
Q.
Let
z
1
,
z
2
,
z
3
,
z
4
are four points in the Argand plane. If
z
is a point such that
|
z
−
z
1
|
=
|
z
−
z
2
|
=
|
z
−
z
3
|
=
|
z
−
z
4
|
, then the points
z
1
,
z
2
,
z
3
,
z
4
can lie on which among the following curves?
Q.
If
z
1
+
z
2
+
z
3
+
z
4
=
0
, then the expression
|
z
1
−
z
2
|
2
+
|
z
2
−
z
3
|
2
+
|
z
3
−
z
4
|
2
+
|
z
4
−
z
1
|
2
−
2
(
|
z
1
|
2
+
|
z
2
|
2
+
|
z
3
|
2
+
|
z
4
|
2
)
is equal to
0
, is and only if,
Q.
Let
4
∑
i
=
1
a
i
=
0
and
4
∑
j
=
1
a
j
z
j
=
0
and
a
1
a
2
|
z
1
−
z
2
|
2
=
a
3
a
4
|
z
3
−
z
4
|
2
.
Then show that
z
1
,
z
2
,
z
3
,
z
4
are concyclic
Q.
If
|
z
1
|
=
|
z
2
|
=
|
z
3
|
=
|
z
4
|
=
1
and
z
1
+
z
2
+
z
3
+
z
4
=
0
, then least value of the expression
E
=
|
z
1
−
z
2
|
2
+
|
z
2
−
z
3
|
2
+
|
z
3
−
z
4
|
2
+
|
z
4
−
z
1
|
2
is
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