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Prove that i^{53} + i^{72} + i^{93} + i^{102} = 2i.

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Prove that i53 + i72 + i93 + i102 = 2i.

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L.H.S = i53 + i72 + i93 + i102

= i + 1 + i + i2

= i+1+i-1

= 2i

L.H.S = R.H.S

Hence proved.

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