Look at the step where fiora sets -1 + √3i to 3√(-1 + √3i)3
In the next step (-1 + √3i)3 is expanded, correctly, to get 8, but then the wrong cube root of 8 is taken. Fiora says the cube root of 8 is 2. If this were the right thing to do here then it would mean that -1 + √3i equals 2, which would be a little unusual to say the least!
The fact is that, in the domain of complex numbers, there are three cube roots of 8, namely 2, -1 - √3i and -1 + √3i. The only valid root here is the last one. It isn't valid to jump from -1 + √3i to (-1 + √3i)3 and then jump back to a different root from the one you came from!
It's like saying -2 squared is 4, the square root of 4 is 2, so we can replace -2 with 2.
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