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Mathematics
Mathematics
Problem
Let
Z
1
=
(
8
+
i
)
sin
θ
+
(
7
+
4
i
)
cos
θ
Z_1 = (8+i)\sin\theta + (7+4i)\cos\theta
Z
1
=
(
8
+
i
)
sin
θ
+
(
7
+
4
i
)
cos
θ
and
Z
2
=
(
1
+
8
i
)
sin
θ
+
(
4
+
7
i
)
cos
θ
Z_2 = (1+8i)\sin\theta + (4+7i)\cos\theta
Z
2
=
(
1
+
8
i
)
sin
θ
+
(
4
+
7
i
)
cos
θ
are two complex numbers. If
Z
1
⋅
Z
2
=
a
+
i
b
Z_1 \cdot Z_2 = a + ib
Z
1
⋅
Z
2
=
a
+
ib
where
a
,
b
∈
R
a, b \in R
a
,
b
∈
R
then the largest value of
(
a
+
b
)
(a+b)
(
a
+
b
)
∀
θ
∈
R
\forall \theta \in R
∀
θ
∈
R
, is (a) 75 (b) 100 (c) 125 (d) 130
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