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Byju's Answer
Standard XII
Mathematics
Modulus of a Complex Number
Let z ∈ℂ be s...
Question
Let
z
∈
C
be such that
|
z
|
<
1
. If
ω
=
5
+
3
z
5
(
1
−
z
)
, then :
A
5
Re
(
ω
)
>
4
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B
5
Re
(
ω
)
>
1
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C
4
Im
(
ω
)
>
5
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D
5
Im
(
ω
)
<
1
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Solution
The correct option is
B
5
Re
(
ω
)
>
1
ω
=
5
+
3
z
5
(
1
−
z
)
⇒
5
ω
−
5
ω
z
=
5
+
3
z
⇒
5
ω
−
5
=
5
ω
z
+
3
z
⇒
z
=
5
(
ω
−
1
)
5
ω
+
3
Since,
|
z
|
<
1
⇒
∣
∣
∣
5
(
ω
−
1
)
5
ω
+
3
∣
∣
∣
<
1
⇒
|
5
(
ω
−
1
)
|
<
|
5
ω
+
3
|
⇒
5
|
(
ω
−
1
)
|
<
5
∣
∣
∣
ω
+
3
5
∣
∣
∣
Let
ω
=
x
+
i
y
⇒
(
x
−
1
)
2
+
y
2
<
(
x
+
3
5
)
2
+
y
2
⇒
x
>
1
5
or,
Re
(
ω
)
>
1
5
Suggest Corrections
131
Similar questions
Q.
Let
z
∈
C
be such that
|
z
|
<
1
. If
ω
=
5
+
3
z
5
(
1
−
z
)
then:
Q.
Let
z
∈
C
be such that
|
z
|
<
1
. If
ω
=
5
+
3
z
5
(
1
−
z
)
, then :
Q.
Let
z
&
ω
be two complex numbers such that
|
z
|
=
1
,
|
ω
|
=
1
and
|
z
+
i
ω
|
=
|
z
−
i
¯
¯
¯
ω
|
=
2
, then
z
equals
Q.
Let
z
and
ω
be two complex numbers such that
|
z
|
≤
1
,
|
ω
|
≤
1
and
|
z
+
i
ω
|
=
|
z
−
i
¯
ω
|
=
2
, then
z
equals
Q.
Let
z
and
ω
two complex number such that
|
z
|
≤
1
,
|
ω
|
≤
1
and
|
z
−
i
ω
|
=
|
z
−
i
¯
¯
¯
ω
|
=
2
, then
z
equals to
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