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)

0

Answer 2

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