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Byju's Answer
Standard XII
Mathematics
Algebra of Complex Numbers
If a2 + 122...
Question
If
(
a
2
+
1
)
2
2
a
−
i
=
x
+
i
y
, then
x
2
+
y
2
is equal to
A
(
a
2
+
1
)
4
4
a
2
+
1
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B
(
a
+
1
)
2
4
a
2
+
1
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C
(
a
2
−
1
2
)
(
4
a
2
−
1
)
2
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D
None of these
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Solution
The correct option is
A
(
a
2
+
1
)
4
4
a
2
+
1
Let,
z
=
x
+
i
y
,
Then,
|
z
|
=
√
x
2
+
y
2
⟹
|
z
|
2
=
x
2
+
y
2
Given
x
+
i
y
=
(
a
2
+
1
)
2
2
a
−
i
⟹
z
=
(
a
2
+
1
)
2
2
a
−
i
Hence,
x
2
+
y
2
=
|
z
|
2
=
∣
∣
(
a
2
+
1
)
2
2
a
−
i
∣
∣
2
x
2
+
y
2
=
|
z
|
2
=
|
(
a
2
+
1
)
2
|
2
|
2
a
−
i
|
2
=
(
a
2
+
1
)
4
4
a
2
+
1
.
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0
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