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

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


=


Since = 1


= i (where n is any positive integer )


=


= -1


= i + 1 + i +


= i+1+i-1


=2i


L.H.S = R.H.S


Hence proved.


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