Complex, yet Faulty

Algebra Level 2

What is the wrong step in the following proof that 1=11 = -1?

  1. Let ww be a complex number such that (w+1)3=(w1)3(w + 1)^3 = (w - 1)^3.

  2. Solving this equation gives w=±i33w = \pm \frac{i \sqrt{3}}{3}.

  3. Since (w+1)3=(w1)3(w + 1)^3 = (w - 1)^3 for our previously mentioned values of ww, cube rooting both sides gives w+1=w1w + 1 = w - 1.

  4. Subtracting ww from both sides gives 1=11 = -1.

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