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JEE Advanced 2013 Paper 2 Mathematics Q9
Mathematics
Problem
Paragraph for Questions 9 and 10 Let
S
=
S
1
∩
S
2
∩
S
3
S=S_1\cap S_2\cap S_3
S
=
S
1
∩
S
2
∩
S
3
, where
S
1
=
{
z
∈
C
:
∣
z
∣
<
4
}
S_1=\{z\in\mathbb C:|z|<4\}
S
1
=
{
z
∈
C
:
∣
z
∣
<
4
}
,
S
2
=
{
z
∈
C
:
Im
[
z
−
1
+
3
i
1
−
3
i
]
>
0
}
S_2=\left\{z\in\mathbb C:\operatorname{Im}\left[\dfrac{z-1+\sqrt3 i}{1-\sqrt3 i}\right]>0\right\}
S
2
=
{
z
∈
C
:
Im
[
1
−
3
i
z
−
1
+
3
i
]
>
0
}
and
S
3
=
{
z
∈
C
:
Re
z
>
0
}
S_3=\{z\in\mathbb C:\operatorname{Re}z>0\}
S
3
=
{
z
∈
C
:
Re
z
>
0
}
. Area of
S
S
S
=
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