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

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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)