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📰 Question: Let $ z^4 + z^2 + 1 = 0 $. Express the maximum imaginary part of a root as $ \sin \theta $, where $ \theta \in [0^\circ, 360^\circ] $, reflecting harmonic analysis in linguistic frequency models. 📰 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 $. 📰 \boxed{60^\circ} 📰 Bootylicious Meaning 2730453 📰 Zoom Mac Os Download 6889471 📰 Selenium Python 📰 Test Water For Ph 2888297 📰 Watch Tv Verizon Fios 📰 Join Thousands Whore Raising Productivity Microsoft 365 For Personal Usenow With Maximum Power 7101973 📰 Step By Step How To Capture Stunning Pc Screenshots Every Time 8334087 📰 2 Squared Secrets Every Student Should Know Before You Graduate 5558660 📰 Unlock Seamless Login Connecteam Login Secrets Revealed 8419587 📰 Survival Karts 📰 Meaning Erp System 📰 How Long Is The Indy 500 Parade 4985355 📰 Nick Sortor Unlocks Secrets You Never Imagined Lies Behind His Protected Methods 1344976 📰 You Wont Believe How This Palette Transforms Your Art 6237677 📰 Love Love Japanese 2588115