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Olympiad
Easy
Algebra
10–12
What is
(
1
+
i
)
10
(1 + i)^{10}
(
1
+
i
)
10
, where
i
2
=
−
1
i^{2} = -1
i
2
=
−
1
?
Quanto vale
(
1
+
i
)
10
(1 + i)^{10}
(
1
+
i
)
10
, onde
i
2
=
−
1
i^{2} = -1
i
2
=
−
1
?
Answer options
A.
32
32
32
B.
32
i
32i
32
i
C.
−
32
i
-32i
−
32
i
D.
−
32
-32
−
32
Check Answer
Solution
Step 1 of 3
1.
First
(
1
+
i
)
2
=
1
+
2
i
+
i
2
=
2
i
(1 + i)^{2} = 1 + 2i + i^{2} = 2i
(
1
+
i
)
2
=
1
+
2
i
+
i
2
=
2
i
.
Next step
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