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Evaluate (i^57 + i^70 + i^91 + i^101 + i^104).

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Evaluate (i57 + i70 + i91 + i101 + i104).

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We have, i57 + i70 + i91 + i101 + i104

= (i4)14.i + (i4)17.i2 + (i4)22.i3 + (i4)25.i + (i4)26

We know that, i4 = 1

⇒ (1)14.i + (1)17.i2 + (1)22.i3 + (1)25.i + (1)26

= i + i2 + i3 + i +1

= i -1 - i + i +1

= i

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