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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Complex Number

NDA 2021 · Mathematics · Complex Number

If x^2+x+1=0 , then what is the value of x^ 199 +x^ 200 +x^ 201 ?

If x2+x+1=0x^2+x+1=0, then what is the value of x199+x200+x201?x^{199}+x^{200}+x^{201} ?

Options

  1. A-1
  2. B0
  3. C1
  4. D3

Correct answer

B. 0

Step-by-step solution

 Given that x2+x+1=0∴x199+x200+x201=x199+x199⋅x+x199⋅x2=x199[1+x+x2]=x199×0=0\begin{aligned} & \text{ Given that } x^2+x+1=0 \\ & \therefore x^{199}+x^{200}+x^{201}=x^{199}+x^{199} \cdot x+x^{199} \cdot x^2 \\ & =x^{199}\left[1+x+x^2\right]=x^{199} \times 0=0\end{aligned}
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