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Find all values of z such that z^4 - 4z^2 +4 = 0.

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$Replace\ z^2\ with\ x.$

$x^2-4x+4=0$

       p          q

$x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ x=2\pm \sqrt{2^2-4}\\ x=2$

$Replace\ x\ with\ z ^ 2.$

$z^2=2\\ z=\pm \sqrt{2}$

$z\in \{-\sqrt{2},\sqrt{2}\}$

$z\in \{-1.414,1.414\}$

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