TS EAMCET · Maths · Complex Number
\(i^2+i^3+\ldots+i^{4000}=\)
- A 1
- B 0
- C \(i\)
- D \(-i\)
Answer & Solution
Correct Answer
(D) \(-i\)
Step-by-step Solution
Detailed explanation
\(\because 1^n+i^{n+1}+i^{n+2}+i^{n+3}=0, \forall n \in\) Integer So, \(i^2+i^3+i^4+\ldots+i^{4000}\) \[ =-i+\left[i+i^2+i^3+\ldots+i^{4000}\right]=-i \]
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