Complex NumbersHard

Question

The value of sum (in + in + 1), where i = √-1 equals

Options

A.i
B.i - 1
C.-i
D.0

Solution

     (in + in + 1) = in(1 + i) = (1 + i) in
= (1 + i) = (1+ i2 + i3 + ......+ i13) = (1 + i)
= (1+ i)i = -1+ i
Alternate Solution
Since, sum of any four consecutive powers of iota is zero.
∴ (in + in+1) = (i + i2 + ...... + i13)
+ (i2 + i3+ .......+i14) = i + i13 + ......+ i14

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