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AIEEE 2010 Solved Paper
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© examsnet.com
Question : 62
Total: 89
The number of complex numbers
z
such that
|
z
−
1
|
=
|
z
+
1
|
=
|
z
−
i
|
equals
1
2
∞
0
Validate
Solution:
Let
z
=
x
+
i
y
|
z
−
1
|
=
|
z
+
1
|
(
x
−
1
)
2
+
y
2
=
(
x
+
1
)
2
+
y
2
⇒
Re
z
=
0
⇒
x
=
0
|
z
−
1
|
=
|
z
−
i
|
(
x
−
1
)
2
+
y
2
=
x
2
+
(
y
−
1
)
2
⇒
x
=
y
|
z
+
1
|
=
|
z
−
i
|
(
x
+
1
)
2
+
y
2
=
x
2
+
(
y
−
1
)
2
Only
(
0
,
0
)
will satisfy all conditions.
⇒
Number of complex number
z
=
1
© examsnet.com
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