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Byju's Answer
Standard XII
Mathematics
Complex Numbers
Find the valu...
Question
Find the value of
cos
(
log
i
i
)
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Solution
Let
a
+
i
b
=
sin
(
log
i
i
)
=
sin
(
i
log
i
)
=
sin
(
i
(
log
|
i
|
+
i
a
m
p
(
i
)
)
)
…
(
i
=
|
i
|
a
m
p
(
i
)
)
=
sin
(
i
(
0
+
i
π
2
)
)
=
sin
(
0
+
i
2
π
2
)
=
sin
(
0
−
π
2
)
a
+
i
b
=
−
1
⇒
a
=
−
1
,
b
=
0
∴
sin
(
log
i
i
)
=
−
1
+
0
=
−
1
Now
cos
(
log
i
i
)
=
√
1
−
sin
2
(
log
i
i
)
=
√
1
−
1
=
0
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