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Mathematics
Problem
Let
Z
i
{
i
=
1
,
2
,
3
,
4
}
Z_i\ \{i = 1, 2, 3, 4\}
Z
i
{
i
=
1
,
2
,
3
,
4
}
represent the vertices of a square all of which lies on sides of a triangle with vertices
(
0
,
0
)
,
(
2
,
1
)
(0, 0), (2, 1)
(
0
,
0
)
,
(
2
,
1
)
and
(
3
,
0
)
(3, 0)
(
3
,
0
)
. Given that
Z
1
Z_1
Z
1
and
Z
2
Z_2
Z
2
are real. If
Z
3
=
a
+
i
b
,
Z
4
=
c
+
i
d
,
a
,
b
,
c
,
d
∈
R
Z_3 = a + ib, Z_4 = c + id, a, b, c, d \in \mathbb{R}
Z
3
=
a
+
ib
,
Z
4
=
c
+
i
d
,
a
,
b
,
c
,
d
∈
R
, then match List-I with List-II.
List - I
Code
Expression
(P)
a
+
c
a + c
a
+
c
(Q)
a
c
ac
a
c
(R)
b
+
d
b + d
b
+
d
(S)
b
d
bd
b
d
List - II
Code
Value
(1)
9
/
16
9/16
9/16
(2)
3
/
2
3/2
3/2
(3)
27
/
8
27/8
27/8
(4)
15
/
4
15/4
15/4
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