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Evaluate (1 + i^10 + i^20 + i^30).

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Evaluate (1 + i10 + i20 + i30).

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We have, 1 + i10 + i20 + i30

= 1 + (i4)2 .i2 + (i4)5 + (i4)7 .i2

We know that, i4 = 1

⇒ 1 + (1)2 .i2 + (1)5 + (1)7 .i2 = 1 + i2 + 1 + i2 = 1 -1 + 1 -1 = 0

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