Q. 3 B4.2( 15 Votes )

# Find the value of following expression:

i^{30} + i^{80} + i^{120}

Answer :

i^{30} + i^{80} + i^{120} = i^{(28 + 2)} + i^{80} + i^{120}

= (i^{4})^{7} × i^{2} + (i^{4})^{20} + (i^{4})^{30}

= – 1 + 1 + 1 = 1

[since i^{4} = 1, i^{2} = – 1]

i^{30} + i^{80} + i^{120} = 1

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