Simplify ( 1 + i )^6
Answers
Enter a problem ...
Trigonometry Examples
Popular Problems Trigonometry Simplify (1 + i) ^ 6
(
1
+
i
)
6
Use the Binomial Theorem .
1
6
+
6
⋅
1
5
i
+
15
⋅
1
4
i
two
+
20
⋅
1
3
i
3
+
15
⋅
1
two
i
4
+
6
⋅
1
i
5
+
i
6
Simplify terms .
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Simplify each term .
Tap for fewer steps ...
One to any power is one.
1
+
6
⋅
1
5
i
+
15
⋅
1
4
i
two
+
20
⋅
1
3
i
3
+
15
⋅
1
two
i
4
+
6
⋅
1
i
5
+
i
6
One to any power is one.
1
+
6
⋅
1
i
+
15
⋅
1
4
i
two
+
20
⋅
1
3
i
3
+
15
⋅
1
two
i
4
+
6
⋅
1
i
5
+
i
6
Multiply
6
by
1
.
1
+
6
i
+
15
⋅
1
4
i
two
+
20
⋅
1
3
i
3
+
15
⋅
1
two
i
4
+
6
⋅
1
i
5
+
i
6
One to any power is one.
1
+
6
i
+
15
⋅
1
i
two
+
20
⋅
1
3
i
3
+
15
⋅
1
two
i
4
+
6
⋅
1
i
5
+
i
6
Multiply
15
by
1
.
1
+
6
i
+
15
i
two
+
20
⋅
1
3
i
3
+
15
⋅
1
two
i
4
+
6
⋅
1
i
5
+
i
6
Rewrite
i
two
at
-
1
.
1
+
6
i
+
15
⋅
−
1
+
20
⋅
1
3
i
3
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
Multiply
15
by
−
1
.
1
+
6
i
−
15
+
20
⋅
1
3
i
3
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
One to any power is one.
1
+
6
i
−
15
+
20
⋅
1
i
3
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
Multiply
20
by
1
.
1
+
6
i
−
15
+
20
i
3
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
Factor out
i
2
.
1
+
6
i
−
15
+
20
(
i
2
⋅
i
)
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
Rewrite
i
2
at
−
1
.
1
+
6
i
−
15
+
20
(
−
1
⋅
i
)
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
Rewrite
−
1
i
at
−
i
.
1
+
6
i
−
15
+
20
(
−
i
)
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
Multiply
−
1
by
20
.
1
+
6
i
−
15
−
20
i
+
15
⋅
1
2
i
4
+
6
⋅
1
i
5
+
i
6
One to any power is one.
1
+
6
i
−
15
−
20
i
+
15
⋅
1
i
4
+
6
⋅
1
i
5
+
i
6
Multiply
15
by
1
.
1
+
6
i
−
15
−
20
i
+
15
i
4
+
6
⋅
1
i
5
+
i
6
Rewrite
i
4
at
1
.
Tap for fewer steps ...
Rewrite
i
4
at
(
i
2
)
two
.
1
+
6
i
−
15
−
20
i
+
15
(
i
2
)
2
+
6
⋅
1
i
5
+
i
6
Rewrite
i
two
at
−
1
.
1
+
6
i
−
15
-
20
i
+
15
(
-
1
)
two
+
6
⋅
1
i
5
+
i
6
Raise
-
1
to the power of
two
.
1
+
6
i
-
15
-
20
i
+
15
⋅
1
+
6
⋅
1
i
5
+
i
6
Multiply
15
by
1
.
1
+
6
i
-
15
-
20
i
+
15
+
6
⋅
1
i
5
+
i
6
Multiply
6
by
1
.
1
+
6
i
-
15
-
20
i
+
15
+
6
i
5
+
i
6
Factor out
i
4
.
1
+
6
i
-
15
-
20
i
+
15
+
6
(
i
4
i
)
+
i
6
Rewrite
i
4
at
1
.
Tap for fewer steps ...
Rewrite
i
4
at
(
i
two
)
two
.
1
+
6
i
-
15
-
20
i
+
15
+
6
(
(
i
two
)
two
i
)
+
i
6
Rewrite
i
two
at
-
1
.
1
+
6
i
-
15
-
20
i
+
15
+
6
(
(
-
1
)
two
i
)
+
i
6
Raise
-
1
to the power of
two
.
1
+
6
i
-
15
-
20
i
+
15
+
6
(
1
i
)
+
i
6
Multiply
i
by
1
.
1
+
6
i
−
15
−
20
i
+
15
+
6
i
+
i
6
Factor out
i
4
.
1
+
6
i
−
15
−
20
i
+
15
+
6
i
+
i
4
i
2
Rewrite
i
4
at
1
.
Tap for fewer steps ...
Rewrite
i
4
at
(
i
two
)
two
.
1
+
6
i
-
15
-
20
i
+
15
+
6
i
+
(
i
two
)
two
i
two
Rewrite
i
two
at
-
1
.
1
+
6
i
-
15
-
20
i
+
15
+
6
i
+
(
-
1
)
two
i
two
Raise
-
1
to the power of
two
.
1
+
6
i
-
15
-
20
i
+
15
+
6
i
+
1
i
two
Multiply
i
2
by
1
.
1
+
6
i
−
15
−
20
i
+
15
+
6
i
+
i
2
Rewrite
i
2
at
−
1
.
1
+
6
i
−
15
−
20
i
+
15
+
6
i
−
1
Simplify by adding terms .
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Subtract
15
from
1
.
-
14
+
6
i
-
20
i
+
15
+
6
i
-
1
Simplify by adding and subtracting.
Tap for fewer steps ...
Add
-
14
and
15
.
1
+
6
i
-
20
i
+
6
i
-
1
Subtract
1
from
1
.
0
+
6
i
-
20
i
+
6
i
Add
0
and
6
i
.
6
i
-
20
i
+
6
i
Subtract
20
i
from
6
i
.
-
14
i
+
6
i
Add
-
14
i
and
6
i
.
-
8
i