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Show that (1/√2 + i/√2)^10 + (1/√2 - i/√2)^10 = 0

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Show that (1/√2 + i/√2)10 + (1/√2 - i/√2)10 = 0

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(1/√2 + i/√2)2 = 1/2 + 2(1/√2)(i/√2) + i2/2

= 1/2 + i - 1/2 = i

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