# Complex, yet Faulty

**Algebra**Level 2

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

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

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

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

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