Question

Value of $i^n+i^{n+1}+i^{n+2}+i^{n+3}$, when $n\in I$ is equal to

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

The correct option is C $0$

$i^n+i^{n+1}+i^{n+2}+i^{n+3}$
$=i^n+i^n.i+i^n.i^2+i^n.i^3$
$=i^n+i^n.i-i^n-i.i^n=0$

$\text{Alternate Solution}$
As $n,n+1,n+2,n+3$ are four consecutive integers.
$\because$ Sum of any four consecutive integral powers of $i$ is zero.
So, $i^n+i^{n+1}+i^{n+2}+i^{n+3}=0$