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📰 Solution: Using De Moivre's Theorem, $ z^n = \cos\left(n\theta\right) + i \sin\left(n\theta\right) $. Here, $ z = \cos\left(\frac{\pi}{6}\right) + i \sin\left(\frac{\pi}{6}\right) $, so $ z^6 = \cos\left(6 \cdot \frac{\pi}{6}\right) + i \sin\left(6 \cdot \frac{\pi}{6}\right) = \cos(\pi) + i \sin(\pi) $. Evaluating, $ \cos(\pi) = -1 $ and $ \sin(\pi) = 0 $, so $ z^6 = -1 + 0i $. 📰 \boxed{-1} 📰 Question: A pharmacologist models the decay of a drug's effectiveness with $ D(t) = D_0 \cdot 2^{-t/12} $. Determine the time $ t $ when the remaining dose is $ \frac{1}{8}D_0 $, rounded to two decimal places. 📰 Finally Revealed Who Is Covered By Medicaid Dont Miss This Essential Guide 6807173 📰 From Casual Chic To Night Glam Long Sleeve Dresses That Dominate Every Occasion 6353522 📰 Calories In The White Of An Egg 3157141 📰 A Man On The Inside Cast 3344797 📰 Sql Query For Union 9430532 📰 How A 1992 Film Changed The Way We Think About Identity Grief And Love Forever 6880887 📰 Ping Ping Game 1277570 📰 Coreweave Stock News Whats Triggering The Trend That Could Shape The Market 8559385 📰 Youll Never Unfire Again With This Flame Perfect For Every Mood This Out Stuns 7916797 📰 Discover How To Unlock Your Cusip With Our Secret Lookup Tool 3660634 📰 Estates Of Richardson Richardson Tx 7606357 📰 Press The Button Game 9413327 📰 You Wont Believe The Hidden Truths Of Their Bedroom Bond 9156483 📰 France Yarborough Unveiled The Shocking Truth Behind Her Daring Life Legacy 1605341 📰 Nokia Stock Starts Surgecould It Be The Next Tech Giant Find Out Now 9297360