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Byju's Answer
Standard XII
Mathematics
Properties of Modulus
If z and w be...
Question
If
z
and
w
be two complex numbers such that
|
z
|
≤
1
,
|
w
|
≤
1
and
|
z
+
i
w
|
=
|
z
−
i
¯
¯¯
¯
w
|
=
2
,
then
A
|
z
|
=
|
w
|
=
1
2
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B
|
z
|
=
1
2
,
|
w
|
=
3
4
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C
|
z
|
=
|
w
|
=
3
4
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D
|
z
|
=
|
w
|
=
1
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Solution
The correct option is
D
|
z
|
=
|
w
|
=
1
∵
|
z
+
i
w
|
≤
|
z
|
+
|
i
w
|
⇒
2
≤
|
z
|
+
|
i
|
|
w
|
⇒
|
z
|
+
|
w
|
≥
2
But from given condition,
|
z
|
+
|
w
|
≤
2
∴
|
z
|
=
|
w
|
=
1
Suggest Corrections
0
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Q.
If
z
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|
z
|
≤
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,
|
w
|
≤
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and
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Let z & w be two complex numbers such that
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and
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|
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,
|
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|
≤
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Properties of Modulus
Standard XII Mathematics
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