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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Complex Number

NDA 2021 · Mathematics · Complex Number

If i= -1 , then how many values does i^ -2 n have for different n ∈...

If i=−1i=\sqrt{-1}, then how many values does i−2ni^{-2 n} have for different n∈Zn \in \mathbb{Z} ?

Options

  1. AOne
  2. BTwo
  3. CFour
  4. DInfinite

Correct answer

B. Two

Step-by-step solution

i−2n=1i2n=(1i2)n=(−1)n∴i−2n={1 when n is  even  −1 when n is  odd  \begin{aligned} & i^{-2 n}=\frac{1}{i^{2 n}}=\left(\frac{1}{i^2}\right)^n=(-1)^n \\ & \therefore i^{-2 n}=\left\{\begin{array}{l}1 \text{ when } n \text{\text{ is }\text{ even } } \\ -1 \text{ when } n \text{\text{ is }\text{ odd } }\end{array}\right.\end{aligned}
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