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UPSC NDA Math Model Paper 4
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© examsnet.com
Question : 111
Total: 120
Evaluate the expression
(
√
2
+
i
√
2
2
)
64
e
i
.
16
π
−
e
i
.
π
∕
16
e
i
.
8
π
−
e
i
.
π
∕
8
Validate
Solution:
The given expression:
(
√
2
+
i
√
2
2
)
64
can re-written as
=
(
√
2
∕
2
+
i
√
2
∕
2
)
64
=
(
1
∕
√
2
+
i
1
∕
√
2
)
64
As we know that
sin
π
∕
4
=
1
∕
√
2
=
cos
π
∕
4
So, we can write the given expression
(
√
2
+
i
√
2
2
)
64
as
=
(
cos
π
∕
4
+
i
sin
π
∕
4
)
64
As we know that,
e
i
.
θ
=
cos
θ
+
i
sin
θ
⇒
(
cos
π
∕
4
+
i
sin
π
∕
4
)
64
=
(
e
i
.
π
∕
4
)
64
⇒
(
cos
π
∕
4
+
i
sin
π
∕
4
)
64
=
e
i
.
16
π
© examsnet.com
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