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Standard XII
Mathematics
Complex Numbers
Question
If
z
=
(
i
)
(
i
)
(
i
)
where
i
=
√
−
1
, then |z| is equal to
e
−
π
1
e
−
π
/
2
None of these
A
e
−
π
/
2
B
e
−
π
C
1
D
None of these
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Solution
Verified by Toppr
l
o
g
(
z
)
=
i
i
l
o
g
(
i
)
=
e
i
π
2
.
i
l
o
g
(
e
i
π
2
)
=
e
−
π
2
i
π
2
Now
e
−
π
2
(
π
2
)
is constant.
Therefore
e
−
π
2
(
π
2
)
=
λ
l
o
g
(
z
)
=
λ
(
i
)
z
=
e
λ
i
⇒
|
z
|
=
1
Hence, option 'A' is correct.
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Similar Questions
Q1
If
z
=
(
i
)
(
i
)
(
i
)
, where i =
√
−
1
, then |z| is equal to: