Q90 / 180 · KCET 2016 · Mathematics

The simplified form of \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3} \) is

Correct answer
A
\( 0 \)
B
\( 11 \)
C
\( -1 \)
D
10

Solution

Given \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3} \) \( =i^{n}\left(1+i+i^{2}+i^{3}\right) \) \( =i^{n}(1+i-1-i)=0 \)

Hence, the correct answer is option: 'A'.

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