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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. 📰 Breaking Email Service Providers Unveil Game Changing 2025 Industry News You Cant Miss 8457837 📰 Hilum Of Kidney 9963614 📰 Headband For Men 7331501 📰 Listen This Timewatts Secret Weapon Is Revolutionizing Everything 5620783 📰 How Many Oz In 1 Liter 8815108 📰 Quad Textwith Mathbfa Langle 2 1 3 Rangle Mathbfb Langle 4 5 1 Rangle 5258437 📰 Tablet Magazine Revealed The 7 Hottest Tech Gadgets You Need To Know 11987 📰 4 Breaking Zoominfo News Reveals The Shocking Connection Changing Everything 2277026 📰 Cast Of The Movie The Break Up 2580849 📰 Cap One Stock 7289243 📰 Guns Up Game 1242504 📰 Epic Gm My Reports 6231529 📰 Guaranteed Hack Bypass Microsoft Account In Windows 11 Without Getting Locked Out 3347451 📰 Grimheds True Truth Secrets To Control Your Darkest Desires 7876077 📰 Tylenol Recall Alert Is Your Medicine Sabotaging Your Health You Wont Believe Whats Inside 6957639