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Other
Engineering Mathematics
Complex Function ( Limit, Analytic Function)
Let j=√-1. Th...
Question
Let
j
=
√
−
1
. Then one value of
j
j
is
A
√
3
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B
−
1
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C
√
1
2
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D
e
−
π
2
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Solution
The correct option is
D
e
−
π
2
We know that
i
=
c
o
s
π
2
+
i
s
i
n
π
2
=
e
i
π
2
So,
i
i
=
⎛
⎝
e
i
π
2
⎞
⎠
i
=
e
−
π
2
Suggest Corrections
0
Similar questions
Q.
Let
I
n
=
1
∫
0
x
n
x
2012
−
1
d
x
,
J
n
=
1
∫
0
x
n
x
2013
+
1
d
x
for all
n
>
2012
,
n
∈
N
and matrix
A
=
(
a
i
j
)
3
×
3
,
where
a
i
j
=
{
I
2012
+
i
−
I
i
,
i
=
j
0
,
i
≠
j
and matrix
B
=
(
b
i
j
)
3
×
3
,
where
b
i
j
=
{
J
2016
+
j
+
J
j
+
3
,
i
=
j
0
,
i
≠
j
.
Then the value of
trace
(
A
−
1
)
+
|
B
−
1
|
is
Q.
If
i
,
j
,
k
are the unit vectors and mutually perpendicular, then the value of
[
i
−
j
j
−
k
k
−
i
]
=
Q.
If
a
→
=
3
i
^
-
j
^
+
2
k
^
and
b
→
=
2
i
^
+
j
^
-
k
^
,
then find
a
→
×
b
→
a
→
.
Q.
If
a
→
=
i
^
-
j
^
and
b
→
=
j
^
+
k
^
,
then
a
→
×
b
→
2
+
a
→
.
b
→
2
=
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
.
Q.
Let
a
→
=
5
i
^
-
j
^
+
7
k
^
a
n
d
b
→
=
i
^
-
j
^
+
λ
k
^
.
Find λ such that
a
→
+
b
→
is orthogonal to
a
→
-
b
→
.
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