Question

The simplified form of $i^n+i^{n+1}+i^{n+2}+i^{n+3}$ is

• A. 0
• B. 1
• C. -1
• D. i

Answer 1

Answer: (A)

We have, $i^n+i^{n+1}+i^{n+2}+i^{n+3}$
$=i^n\left(1+i+i^2+i^3\right)$
$=i^n(1+i-1-i)$
$\left[\because i^2=-1\text{ and }{i}^3=-i\right]$
$=i^n\times 0=0$