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A complex number $\alpha \in \mathbb{C}$ is called algebraic if there is a non-zero polynomial $P(x) \in \mathbb{Q}\left[x\right]$ with rational coefficients such that $P(\alpha)=0$. Which of the following statements is true?

  1. There are only finitely many algebraic numbers.
  2. All complex numbers are algebraic.
  3. $\sin \frac{\pi}{3}+ \cos \frac{\pi}{4}$ is algebraic.
  4. None of the above.
in Set Theory & Algebra by Boss (29.9k points) | 78 views

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