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Evaluate: (i^77 + i^70+i^87 + i^414)^3

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Evaluate: (i77 + i70+i87 + i414)3

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(i77 + i70+i87 + i414)3

= [(i4 )19i + (i4 )17 i2 + (i4 )21i3 + (i4 )103i2 ]3

 = [ i+i2 + i3 + i2 ] 3    [∵i4 = 1] 

= [ i− 1 − i − 1] 3      [∵ i2 = −1and i3 = −]

 = [-2]3 = -8

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