Complex, yet Faulty

Algebra Level 2

What is the wrong step in the following proof that \(1 = -1\)?

  1. Let \(w\) be a complex number such that \((w + 1)^3 = (w - 1)^3\).

  2. Solving this equation gives \(w = \pm \frac{i \sqrt{3}}{3}\).

  3. Since \((w + 1)^3 = (w - 1)^3\) for our previously mentioned values of \(w\), cube rooting both sides gives \(w + 1 = w - 1\).

  4. Subtracting \(w\) from both sides gives \(1 = -1\).

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