\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Decide whether the following pairs are coprime in \(\mathbb{R}[X]\), by computing their common complex roots (in \(\mathbb{C}\)).
  1. \(A = X^2 + 1\), \(B = X^2 - 2 X + 2\).
  2. \(A = X^4 + 1\), \(B = X^2 + 1\).

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