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Test Index
Complex Numbers Part 1
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Section:
Mathematics
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© examsnet.com
Question : 15
Total: 100
The equation
arg
(
z
−
1
z
+
1
)
=
Ï€
4
represents a circle with
[26 Aug 2021 Shift 1]
centre at
(
0
,
−
1
)
and radius
√
2
centre at
(
0
,
1
)
and radius
√
2
centre at
(
0
,
0
)
and radius
√
2
centre at
(
0
,
1
)
and radius 2
Validate
Solution:
We have,
arg
(
z
−
1
z
+
1
)
=
Ï€
4
⇒
arg
(
z
−
1
)
−
arg
(
z
+
1
)
=
Ï€
4
Let
z
=
x
+
i
y
arg
[
(
x
−
1
)
+
i
y
]
−
arg
[
(
x
+
1
)
+
i
y
]
=
Ï€
4
⇒
tan
−
1
(
y
x
−
1
)
−
tan
−
1
(
y
x
+
1
)
=
Ï€
4
⇒
(
y
x
−
1
−
y
x
+
1
1
+
y
x
−
1
.
y
x
+
1
)
=
tan
‌
Ï€
4
⇒
y
(
x
+
1
)
−
y
(
x
−
1
)
(
x
2
−
1
)
+
y
2
=
1
⇒
2
y
=
x
2
+
y
2
−
1
⇒
x
2
+
y
2
−
2
y
−
1
=
0
⇒
x
2
+
(
y
−
1
)
2
=
2
⇒
x
2
+
(
y
−
1
)
2
=
(
√
2
)
2
Which is a circle with Centre
(
0
,
1
)
and Radius
=
√
2
units
© examsnet.com
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