znajdź pierwsiatki z biorze liczb zespolonych

[tommy007]

\(\displaystyle{ z^4-2z^2+4}\)

[przemk20]

\(\displaystyle{ z^4-2z^2+4 = (z^4 - 4z^2+4) + 2z^2 = (z^2-2)^2 - (i\sqrt{2}z)^2 =
(z^2 - i \sqrt{2}z-2)(z^2+ i \sqrt{2}z-2) \\
\Delta_{12} = -2+8 = 6 \\
z_{11} = \frac{i \sqrt{2} - \sqrt{6}}{2}, \ \ \ z_{12} = \frac{i \sqrt{2} + \sqrt{6}}{2}, \\
z_{21} = \frac{-i \sqrt{2} - \sqrt{6}}{2}, \ \ \ z_{22} = \frac{-i \sqrt{2} + \sqrt{6}}{2},}\)