i^2+i^3+ +i^ 4000 = - Vidyadip

MCQ

$i^2+i^3+\ldots+i^{4000}=$

A
1
B
$0$
C
i
✓
$-i$

✓

Answer

Correct option: D.

$-i$

(D)
$i^2+i^3+\ldots+i^{4000}$
$=i+i^2+i^3+\ldots+i^{4000}-i$
$=\left(i+i^2+i^3+i^4\right)+\ldots$ $+\left( i ^{3097}+ i ^{3098}+ i ^{3099}+ i ^{4000}\right)- i$
$=0+\ldots+0- i$ $\ldots\left[\because i ^{ n }+ i ^{ n +1}+ i ^{ n +2}+ i ^{ n +3}=0\right]$
$=- i$

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