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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Complex Number

NDA 2023 · Mathematics · Complex Number

Consider equation-I: z^3+2 z^2+2 z+1=0 and equation -II: z^ 1985...

Consider equation-I: z3+2z2+2z+1=0z^3+2 z^2+2 z+1=0 and equation -II: z1985+z100+1=0z^{1985}+z^{100}+1=0 Which of the following is a root of equation-I?

Options

  1. A– 1
  2. B– ω
  3. C−ω2-\omega^2
  4. Dω

Correct answer

D. ω

Step-by-step solution

Since, the given equation-II is z1985+z100+1=0z^{1985}+z^{100}+1=0 If z=−1,−1+1+1≠0z=-1,-1+1+1 \neq 0 If z=−ω,ω1985+ω100+1≠0z=-\omega, \omega^{1985}+\omega^{100}+1 \neq 0 If z=−ω2,(−ω2)1985+(−ω2)100+1≠0z=-\omega^2,\left(-\omega^2\right)^{1985}+\left(-\omega^2\right)^{100}+1 \neq 0 If z=ω,ω1985+ω100+1=0z=\omega, \omega^{1985}+\omega^{100}+1=0 So option (D) is correct.
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