SOLUTION: Find (1/sqrt2 + i/sqrt2)^8 -8 256 8 1 None

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Question 304856: Find (1/sqrt2 + i/sqrt2)^8
-8
256
8
1
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find (1/sqrt(2) + i/sqrt(2))^8
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= [(1+i)/sqrt(2)]^8
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= (1/16)[8C8(1)^8(i)^0 + 8C7(i^1) + 8C6(i^2) + 8C5(i^3) + 8C4(i^4) + 8C3(i^5)
+ 8C2(i^6) + 8C1(i^7) + 8C0(i^8)]
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= (1/16)[1 + 8i - 28 - 56i + 70 + 56i - 28 -8i + 1]
---
(1/16)(2 - 56 + 70]
(1/16)(16)
= 1
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Cheers,
Stan H.
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-8
256
8
1
None