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Byju's Answer
Standard XII
Mathematics
General Term of Binomial Expansion
i4n + 3 + -i8...
Question
i
4
n
+
3
+
(
−
i
)
8
n
−
3
(
i
)
12
n
−
1
−
i
2
−
16
n
,
n
ε
N
is equal to
A
1 + i
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B
2i
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C
-2i
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D
-1 - i
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Solution
The correct option is
B
-1 - i
Given expression
=
i
3
+
(
−
1
)
(
i
)
−
3
(
−
i
)
−
1
−
(
i
)
2
=
−
i
−
i
i
+
1
=
−
2
i
1
+
i
×
1
−
i
1
−
i
=
−
2
i
−
2
1
+
1
=
−
1
−
i
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0
Similar questions
Q.
What is
(
1
+
i
)
4
n
+
5
(
1
−
i
)
4
n
+
3
equal to, where n is a natural number and
i
=
√
−
1
?
Q.
If
I
1
=
∫
−
5
−
4
e
(
x
+
5
)
2
d
x
and
I
2
=
3
∫
2
/
3
1
/
3
e
(
3
x
−
2
)
2
d
x
then
I
1
+
I
2
equals?
Q.
(
1
+
i
1
−
i
)
2
+
(
1
−
i
1
+
i
)
2
is equal to
Q.
Express the following complex numbers in the standard form a + i b:
(i)
(
1
+
i
)
(
1
+
2
i
)
(ii)
3
+
2
i
-
2
+
i
(iii)
1
(
2
+
i
)
2
(iv)
1
-
i
1
+
i
(v)
(
2
+
i
)
3
2
+
3
i
(vi)
(
1
+
i
)
(
1
+
3
i
)
1
-
i
(vii)
2
+
3
i
4
+
5
i
(viii)
(
1
-
i
)
3
1
-
i
3
(ix)
(
1
+
2
i
)
-
3
(x)
3
-
4
i
(
4
-
2
i
)
(
1
+
i
)
(xi)
1
1
-
4
i
-
2
1
+
i
1
-
4
i
5
+
i
(xii)
5
+
2
i
1
-
2
i
Q.
If
A
=
⎡
⎢ ⎢ ⎢
⎣
−
1
+
i
√
3
2
i
−
1
−
i
√
3
2
i
1
+
i
√
3
2
i
1
−
i
√
3
2
i
⎤
⎥ ⎥ ⎥
⎦
,
i
=
√
−
i
and
f
(
x
)
=
x
2
+
2
, then
f
(
A
)
is equal to
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