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JEE Main 8 Apr 2024 Shift 2 Solved Paper
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© examsnet.com
Question : 6
Total: 90
The sum of all possible values of
θ
∈
[
−
π
,
2
π
]
, for which
1
+
i
cos
θ
1
−
2
i
cos
θ
is purely imaginary, is equal to
[8 Apr 2024 Shift 2]
2
π
3
π
5
π
4
π
Validate
Solution:
👈: Video Solution
Z
=
1
+
i
cos
θ
1
−
2
i
cos
θ
Z
=
−
Z
⇒
1
+
i
cos
θ
1
−
2
i
cos
θ
=
−
(
1
+
i
cos
θ
1
−
2
i
cos
θ
)
(
1
+
i
cos
θ
)
(
1
−
2
i
cos
θ
)
=
−
(
1
−
2
i
cos
θ
)
(
1
+
i
cos
θ
)
(
1
+
i
cos
θ
)
(
1
+
2
i
cos
θ
)
=
−
(
1
−
2
i
cos
θ
)
(
1
−
i
cos
θ
)
1
+
3
i
cos
θ
−
2
cos
2
θ
=
−
(
1
−
3
i
cos
θ
−
2
cos
2
θ
)
2
−
4
cos
2
θ
=
0
⇒
cos
2
θ
=
1
2
⇒
θ
=
−
π
4
,
−
3
π
4
,
π
4
,
3
π
4
,
5
π
4
,
7
π
4
sum
=
3
π
© examsnet.com
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