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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Complex Number

NDA 2010 · Mathematics · Complex Number

If ω is a complex cube root of unity and x=ω^2-ω-2 , then what is...

If ω\omega is a complex cube root of unity and x=ω2−ω−2x=\omega^2-\omega-2, then what is the value of x2+4x+7x^2+4 x+7 ?

Options

  1. A-2
  2. B-1
  3. C0
  4. D1

Correct answer

C. 0

Step-by-step solution

x=w2−w−2x=w^2-w-2 Consider x2+4x+7=(−2w−3)2+4(−2w−3)+7=4w2+4w+4=4(w2+w+1)=4×0=0\begin{aligned} & x^2+4 x+7=(-2 w-3)^2+4(-2 w-3)+7 \\ & =4 w^2+4 w+4=4\left(w^2+w+1\right) \\ & =4 \times 0=0 \end{aligned}
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