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Byju's Answer
Standard XII
Mathematics
Distance Formula Using Complex Numbers
The complex n...
Question
The complex number
z
satisfying the equation
|
z
−
i
|
=
|
z
+
1
|
=
1
is
A
0
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B
1
+
i
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C
−
1
+
i
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D
1
−
i
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Solution
The correct options are
A
0
C
−
1
+
i
Let
z
=
x
+
i
y
|
z
−
i
|
=
|
z
+
1
|
=
1
|
z
−
i
|
=
|
z
+
1
|
⇒
x
2
+
(
y
−
1
)
2
=
(
x
+
1
)
2
+
y
2
⇒
x
2
+
y
2
−
2
y
+
1
=
x
2
+
2
x
+
1
+
y
2
⇒
x
=
−
y
⋯
(
1
)
|
z
+
1
|
=
1
⇒
(
x
+
1
)
2
+
x
2
=
1
[
From
(
1
)
]
⇒
2
x
2
+
2
x
=
0
⇒
x
(
x
+
1
)
=
0
⇒
x
=
0
,
−
1
⇒
y
=
0
,
1
∴
z
=
0
,
−
1
+
i
Suggest Corrections
7
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Q.
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z
1
=
a
+
i
b
&
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2
=
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1
|
=
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R
e
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