[tex]z^4 + 81 = 0\\t = z^2 => \\t^2 + 81 = 0\\t_{12}=\pm 9i\\z^2 = 9i => z_{12} = \pm 3\sqrt{i} = \pm (\frac{3\sqrt{2}}{2} + \frac{3i\sqrt{2}}{2})\\z^2 = -9i => z_{34} = \pm 3i\sqrt{i} = \pm (- \frac{3\sqrt{2}}{2} + \frac{3i\sqrt{2}}{2})\\z \in \{\pm (\frac{3\sqrt{2}}{2} + \frac{3i\sqrt{2}}{2}), \pm(- \frac{3\sqrt{2}}{2} + \frac{3i\sqrt{2}}{2})\}[/tex]
