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.