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Byju's Answer
Standard XII
Mathematics
Properties of Modulus
lf Z1,Z2 ar...
Question
lf
Z
1
,
Z
2
are two unimodular Complex numbers then
∣
∣
∣
1
Z
1
+
1
Z
2
∣
∣
∣
=
A
1
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B
|
Z
1
+
Z
2
|
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C
|
Z
1
|
+
|
Z
2
|
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D
2
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Solution
The correct option is
B
|
Z
1
+
Z
2
|
∣
∣
∣
1
z
1
+
1
z
2
∣
∣
∣
=
∣
∣
∣
z
1
+
z
2
z
1
z
2
∣
∣
∣
=
|
z
1
+
z
2
|
|
z
1
|
|
z
2
|
=
|
z
1
+
z
2
|
1
×
1
=
|
z
1
+
z
2
|
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0
Similar questions
Q.
lf
z
1
and
z
2
are two complex numbers such that
|
z
1
|
=
|
z
2
|
+
|
z
1
−
z
2
|
, then
arg
(
z
1
)
−
arg
(
z
2
)
Q.
Assertion :
If
z
1
≠
z
2
and
|
z
1
+
z
2
|
=
∣
∣
∣
1
z
1
+
1
z
2
∣
∣
∣
then
z
1
z
2
is unimodular.
Reason: Both
z
1
and
z
2
are unimodular.
Q.
If
z
1
and
z
2
are two complex numbers, then prove that
|
z
1
|
+
|
z
2
|
=
∣
∣
∣
z
1
+
z
2
2
+
√
z
1
z
2
∣
∣
∣
+
∣
∣
∣
z
1
+
z
2
2
−
√
z
1
z
2
∣
∣
∣
Q.
For two unimodular complex numbers
z
1
and
z
2
,
[
¯
¯¯¯
¯
z
1
−
z
2
¯
¯¯¯
¯
z
2
z
1
]
−
1
[
z
1
z
2
−
¯
¯¯¯
¯
z
2
¯
¯¯¯
¯
z
1
]
−
1
is equal to
Q.
If
z
1
≠
−
z
2
and
|
z
1
+
z
2
|
=
|
(
1
z
1
)
+
(
1
z
2
)
|
then
Statement 1:
z
1
z
2
is unimodular.
Statement 2: Both
z
1
and
z
2
are unimodular.
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