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📰 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} 📰 Question: If $ \mathbf{a}, \mathbf{b}, \mathbf{c} $ are unit vectors in $ \mathbb{R}^3 $ with $ \mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} = \frac{1}{2} $, find the maximum value of $ \|\mathbf{a} + \mathbf{b} + \mathbf{c}\| $, modeling directional consistency in linguistic feature spaces. 📰 These Knee High Cowboy Boots Are Changing Style Foreversee Why 8790764 📰 Shocked You Never Heard Of Black Tie Optional Heres Why Its Taking Elite Events By Storm 1464439 📰 Mount And Blade Warband Warband 3407391 📰 Actors Of We Bought A Zoo 5754917 📰 Ready Or Not Indir 9138932 📰 Youll Be Hunting For The Perfect Perasuit Jacket After This Look 1970930 📰 Meaning Relevance 6501661 📰 From Humble Beginnings To Legenduncover Wolverines Origins In Men X 2977134 📰 Master Options Trading In Days Unlock Hidden Profits With Our Trading Options Classes Today 992903 📰 Visio Viewer For Mac 5756134 📰 Is Roblox Broken Experts Reveal How Much The Platform Lost 5101817 📰 How Many Calories Is A Double Cheeseburger At Mcdonalds 3599021 📰 Noz Market 1369982 📰 Airline Tickets To St Barts 6562459 📰 Unlock Fluent English With Longman Contemporary The Ultimate Study Tool You Need Now 6412281