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📰 Question: Compute $ \left( \cos \frac{2\pi}{7} + i \sin \frac{2\pi}{7} \right)^{14} + \left( \cos \frac{2\pi}{7} - i \sin \frac{2\pi}{7} \right)^{14} $, a quantity arising in modeling periodic synthetic microbial interactions in subglacial biofilm networks. 📰 Let $ z = \cos \frac{2\pi}{7} + i \sin \frac{2\pi}{7} = e^{i \frac{2\pi}{7}} $. Then its conjugate is $ \overline{z} = \cos \frac{2\pi}{7} - i \sin \frac{2\pi}{7} = e^{-i \frac{2\pi}{7}} $. 📰 z^{14} + \overline{z}^{14} = \left(e^{i \frac{2\pi}{7}}\right)^{14} + \left(e^{-i \frac{2\pi}{7}}\right)^{14} = e^{i 4\pi} + e^{-i 4\pi} 📰 5 Hidden Opportunity Alert When You Can Withdraw Your 401Kdont Miss It 3992495 📰 My Health Savings Bank Of America 6382774 📰 How I Lost My Sunshine And Found Everything I Never Knew I Needed 2894342 📰 Application Control 8047569 📰 Wells Fargo Banck 2411024 📰 Carrot Calories 6652355 📰 Chrones Disease 6366703 📰 4 Double Your Accent Accuracy With These Pro Shortcuts 3683725 📰 The Edge Of Fear What Secret Lies Beyond The Shadows Edge Is Unstoppable 4021374 📰 Ein Kreis Hat Einen Umfang Von 314 Cm Was Ist Sein Radius Verwende Pi Approx 314 5564936 📰 Calculate Exact Measurements In Inchesknow Your Size Like A Pro 438371 📰 Download Youtube Videos Instantly The Best Youtube Downloader For Windows 10 3436673 📰 Jumbo Mortgage 8126975 📰 This Rockford Scanner Catch Could Change How You See Your City Forever 8515391 📰 Pojav Launcher Apk 1948738