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Test Index
JEE Mains 15-Apr-2023 Shift 1 Solved Paper
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© examsnet.com
Question : 4
Total: 90
If the set
{
Re
(
z
−
z
+
z
z
2
−
3
z
+
5
z
)
:
z
∈
C
,
Re
(
z
)
=
3
}
is equal to the interval
(
α
,
β
]
, then
24
(
β
−
α
)
is equal to
[15-Apr-2023 shift 1]
36
27
30
42
Validate
Solution:
Let
z
1
=
(
z
−
z
+
z
z
2
−
3
z
+
5
z
)
Let
z
=
3
+
iy
z
=
3
−
iy
z
1
=
2
i
y
+
(
9
+
y
2
)
2
−
3
(
3
+
i
y
)
+
5
(
3
−
i
y
)
=
9
+
y
2
+
i
(
2
y
)
8
−
8
i
y
=
(
9
+
y
2
)
+
i
(
2
y
)
8
(
1
−
i
y
)
Re
(
z
1
)
=
(
9
+
y
2
)
−
2
y
2
8
(
1
+
y
2
)
=
9
−
y
2
8
(
1
+
y
2
)
=
1
8
[
10
−
(
1
+
y
2
)
(
1
+
y
2
)
]
=
1
8
[
10
(
1
+
y
2
)
−
1
]
1
+
y
2
∈
[
1
,
∞
]
1
1
+
y
2
∈
(
0
,
1
]
10
1
+
y
2
∈
(
0
,
10
]
10
1
+
y
2
−
1
∈
(
−
1
,
9
]
Re
(
z
1
)
∈
(
−
1
8
,
9
8
]
α
=
−
1
8
,
β
=
9
8
24
(
β
−
α
)
=
24
(
9
8
+
1
8
)
=
30
© examsnet.com
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