COMEDK · Maths · 3. Complex Number
If \(i=\sqrt{-1}\) and \(n\) is a positive integer, then \(i^n+i^{n+1}+i^{n+2}+i^{n+3}\) is equal to
- A \(i^n\)
- B 0
- C 1
- D \(i\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
The expression is \(i^n + i^{n+1} + i^{n+2} + i^{n+3}\). Factoring out \(i^n\), we get \(i^n(1 + i + i^2 + i^3)\). Since \(i^2 = -1\) and \(i^3 = -i\), the expression becomes \(i^n(1 + i - 1 - i)\). Simplifying the terms inside the parentheses: \(1 - 1 + i - i = 0\). Therefore,…
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