Question:medium

If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 - 2x + 2 = 0 \), then \( \alpha^{2026} + \beta^{2026} = \)

Show Hint

For roots like \( 1 \pm i \), always remember the argument is \( \pm \pi/4 \). If the power \( n \) is such that \( n\theta \) is an odd multiple of \( \pi/2 \), the sum of the powers of the roots will always be zero.
Updated On: Jul 18, 2026
  • \( -2^{2026} \)
  • \( 2^{1014} \)
  • \( -2^{1014} \)
  • \( 0 \)
Show Solution

The Correct Option is D

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