Q. 144.6( 5 Votes )

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

Answer :

L.H.S = i^{53} + i^{72} + i^{93} + i^{102}

=

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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