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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. 📰 Download Any Youtube Video In Seconds With These Shocking Tips 3994023 📰 Lowrider Comeback 2 The Legend Returnsand You Wont Believe Whats Inside 2277930 📰 Stolen Device Protection Iphone 1225422 📰 Java Se Latest Version 293107 📰 Unlock Exclusive Style Credor Watches That Speed Up Time And Attention Like Never Before 7777536 📰 Yaroas Hidden Secret Why Travelers Are Dropping Everything To Visit Now 7038922 📰 Get Your Ultimate Football Wallpaper Collection Mobile Wallpaper That Rocks Every Game 7238314 📰 Hear About The Breakthrough Voice Agents Are Shaping Todays Voice Tech News 1999208 📰 Vypress Chat 📰 Bifold Concertina Doors Transform Your Space In Seconds Youll Never Turn Back 3053401 📰 Why Artoria Pendragon Is The Hidden Symbol In Modern Myths Legends 9407958 📰 Live Update Ai For Investing And It Gets Worse 📰 How To Create A Fortnite Account 4674005 📰 This Fair Food Goldmine Is Hiding In Plain Sight Learn How To Eat Ethically Today 9936427 📰 Kim Coles 4397999