Answer :

we have, 1 + i10 + i20 + i30

= 1 + (i4)2.i2 + (i4)5 + (i4)7.i2


We know that, i4 = 1


1 + (1)2.i2 + (1)5 + (1)7.i2


= 1 + i2 + 1 + i2


= 1 -1 + 1 -1


= 0


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