Solution: Factor $ z^4 + z^2 + 1 = (z^2 + z + 1)(z^2 - z + 1) = 0 $. Solving $ z^2 + z + 1 = 0 $ gives roots $ z = \frac{-1 \pm i\sqrt{3}}{2} $, with imaginary parts $ \pm \frac{\sqrt{3}}{2} $. Solving $ z^2 - z + 1 = 0 $ gives $ z = \frac{1 \pm i\sqrt{3}}{2} $, with imaginary parts $ \pm \frac{\sqrt{3}}{2} $. The maximum imaginary part is $ \frac{\sqrt{3}}{2} = \sin 60^\circ $.

Sat, 02 May 2026 12:11:17 +0000

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