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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 3 Questions
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© examsnet.com
Question : 9
Total: 100
Let
A
=
{
θ
∈
(
0
,
2
π
)
:
1
+
2
i
s
i
n
θ
1
−
i
s
i
n
θ
.
is purely imaginary
}
. Then the sum of the elements in
A
is.
[8-Apr-2023 shift 2]
π
3
π
4
π
2
π
Validate
Solution:
z
=
1
+
2
i
s
i
n
θ
1
−
i
s
i
n
θ
×
1
+
i
s
i
n
θ
1
+
i
s
i
n
θ
z
=
1
−
2
s
i
n
2
θ
+
i
(
3
s
i
n
θ
)
1
+
s
i
n
2
θ
Re
(
z
)
=
0
1
−
2
s
i
n
2
θ
1
+
s
i
n
2
θ
=
0
s
i
n
θ
=
±
1
√
2
A
=
{
π
4
,
3
π
4
,
5
π
4
,
7
π
4
}
sum
=
4
π
(
Option
3
)
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