+33 I am not the best at explaining, and I don't explain very much(new user and look at my username), so don't go attacking me. (I also skip like a lot of "simple" to me steps)
First, you can factor z^4 - 4z^2 + 4 = 0 into (z^2 -2)^2
I am assuming that you already know this, but i will still "explain"
You can turn z^4 - 4z^2 +4 = 0 into z^4 - 2z^2 - 2z^2 + 4
Then, you notice that you can factor that into z^2(z^2 - 2) -2(z^2 - 2)
Then, you can turn that into (z^2 -2)(z^2-2). Or, (z^2 - 2)^2.
You notice that \(\sqrt{2}\), will work, and -\(\sqrt{2}\).
Because, \((\sqrt{2})^2\)is equal to 0, (2-2)^2 = 0
And \((-\sqrt{2})^2\)is also equal to 2.
I hope this helped?
