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Standard XII
Maths
Question
If
z
−
2
z
+
2
(
z
≠
−
2
)
is purely imaginary then
|
z
|
is equal to
1
3
4
2
A
1
B
2
C
4
D
3
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Solution
Verified by Toppr
Let
z
=
x
+
i
y
Then,
z
−
2
z
+
2
=
x
+
i
y
−
2
x
+
i
y
+
2
=
(
x
−
2
)
+
i
y
(
x
+
2
)
+
i
y
=
[
(
x
−
2
)
+
i
y
]
[
(
x
+
2
)
+
i
y
]
(
x
+
2
)
2
+
y
2
=
(
x
2
+
y
2
−
4
)
+
i
(
4
y
)
(
x
+
2
)
2
+
y
2
Since
z
−
2
z
+
2
is purely imaginary,
∴
x
2
+
y
2
−
4
=
0
⇒
x
2
+
y
2
=
4
⇒
|
z
|
2
=
4
⇒
|
z
|
=
2.
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2
z
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|
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