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UPSC NDA I and II 2020 Math Solved Paper
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© examsnet.com
Question : 1
Total: 120
What is the modulus of the complex number
cos
θ
+
i
sin
θ
cos
θ
−
i
sin
θ
,
where
i
=
√
−
1
?
[NDA-I 2020]
1
2
1
3
2
2
Validate
Solution:
👈: Video Solution
Z
=
cos
θ
+
i
sin
θ
cos
θ
−
i
sin
θ
=
(
cos
θ
+
i
sin
θ
)
(
cos
θ
−
i
sin
θ
)
×
(
cos
θ
+
i
sin
θ
)
(
cos
θ
+
i
sin
θ
)
=
(
cos
θ
+
i
sin
θ
)
2
cos
2
θ
−
(
i
sin
θ
)
2
=
cos
2
θ
+
i
sin
2
θ
cos
2
θ
+
sin
2
θ
=
cos
2
θ
+
i
sin
2
θ
Modulus of Z
=
|
Z
|
=
√
cos
2
(
2
θ
)
+
sin
2
(
2
θ
)
=
1
© examsnet.com
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