KCET · Maths · Complex Number
The simplified form of \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3} \) is
- A \( 0 \)
- B \( 11 \)
- C \( -1 \)
- D 10
Answer & Solution
Correct Answer
(A) \( 0 \)
Step-by-step Solution
Detailed explanation
Given \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3} \)
\( =i^{n}\left(1+i+i^{2}+i^{3}\right) \)
\( =i^{n}(1+i-1-i)=0 \)
\( =i^{n}\left(1+i+i^{2}+i^{3}\right) \)
\( =i^{n}(1+i-1-i)=0 \)
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