# 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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