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JEE Advanced 2013 Paper 2 Mathematics Q1
Mathematics
Problem
Let
w
=
(
3
+
i
)
/
2
w=(\sqrt3+i)/2
w
=
(
3
+
i
)
/2
and
P
=
{
w
n
:
n
=
1
,
2
,
3
,
…
}
P=\{w^n:n=1,2,3,\ldots\}
P
=
{
w
n
:
n
=
1
,
2
,
3
,
…
}
. Further,
H
1
=
{
z
∈
C
:
Re
z
>
1
/
2
}
H_1=\{z\in\mathbb C:\operatorname{Re}z>1/2\}
H
1
=
{
z
∈
C
:
Re
z
>
1/2
}
and
H
2
=
{
z
∈
C
:
Re
z
<
−
1
/
2
}
H_2=\{z\in\mathbb C:\operatorname{Re}z<-1/2\}
H
2
=
{
z
∈
C
:
Re
z
<
−
1/2
}
. If
z
1
∈
P
∩
H
1
z_1\in P\cap H_1
z
1
∈
P
∩
H
1
,
z
2
∈
P
∩
H
2
z_2\in P\cap H_2
z
2
∈
P
∩
H
2
and
O
O
O
represents the origin, then
∠
z
1
O
z
2
\angle z_1Oz_2
∠
z
1
O
z
2
=
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