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📰 Solution: The expression $ \cos x + i\sin x $ corresponds to $ e^{ix} $ on the unit circle in the complex plane. Therefore, $ \cos x + i\sin x + 1 = e^{ix} + 1 $. The modulus is $ |e^{ix} + 1| $. Using the identity $ |e^{ix} + 1| = \sqrt{(\cos x + 1)^2 + \sin^2 x} $, we simplify: 📰 |e^{ix} + 1| = \sqrt{(\cos x + 1)^2 + \sin^2 x} = \sqrt{\cos^2 x + 2\cos x + 1 + \sin^2 x} = \sqrt{2 + 2\cos x} 📰 The minimum value occurs when $ \cos x $ is minimized, i.e., $ \cos x = -1 $: 📰 Get Unstoppable Your Skills With This Hottest Online Simulatorwatch It Go Viral 7676441 📰 Change Drop Down List In Excel 1325619 📰 Niki Skyler 7416717 📰 The 1 Peanut Butter Solution Doctors Swear Byheres How It Works 9186534 📰 Trump Nvidia 7532694 📰 How Many Grams Of Protein In An Egg 1237715 📰 Kid Chissell 2525297 📰 Is This The Cutest Fennec Shand Youve Ever Seen Viral Wildlife Shock Factor Inside 7677120 📰 Surprising Ways To Master Flowchart Creation In Microsoft Visio 9798325 📰 You Wont Believe What This New Blade Movie Will Do To Your Blood 9537473 📰 The Price Of A Stock Increased By 15 To 115 What Was The Original Price 3409486 📰 Usdcnh Gunshot You Wont Believe Whats Happening In The Forex Market Right Now 1290391 📰 Acquisition Oracle Revealed How This Tool Changed Company Buyouts Forever 4912254 📰 Where Do They Sell Labubus 3590911 📰 Battlefield 6 Br Download 9888166