\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
  1. Expand \((x + i)^3\) for any real number \(x\).
  2. Determine for which real value(s) of \(x\) the complex number \((x + i)^3\) is purely imaginary.

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