SOLUTION: Find (1 / sq. rt. 2 + i / sq. rt. 2) ^ 8 a.) -8 b.) 256 c.) 8 d.) 1 e.) None of these

Question 122065: Find (1 / sq. rt. 2 + i / sq. rt. 2) ^ 8

a.) -8
b.) 256
c.) 8
d.) 1
e.) None of these

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

It's very useful to note that and . So the expression is equivalent to

Now we're going to use De Moivre's theorem to solve this problem.

Remember, De Moivre's theorem states:

So using De Moivre's theorem we get

Multiply and to get . Now reduce to get

Take the cosine of to get 1. Take the sine of to get 0.

Remove the zero term

So simplifies to 1.

In other words,

So the answer is D)
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