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📰 Numerator: $ 2(1 + e^{i4\pi/3}) $, denominator: $ 1 - e^{i4\pi/3} $, so $ S = 2 \cdot rac{1 + e^{i4\pi/3}}{1 - e^{i4\pi/3}} $. Multiply numerator and denominator by $ e^{-i2\pi/3} $: 📰 S = 2i \cdot rac{e^{i2\pi/3} + e^{i2\pi/3}}{e^{i2\pi/3} - e^{-i2\pi/3}} = ext{complicated}. 📰 But from earlier general form $ S = rac{2(a^2 + b^2)}{a^2 - b^2} $, and $ |a| = |b| = 1 $, let $ a^2 = z $, $ b^2 = \overline{z} $ (since $ |b^2| = 1 $), but $ b $ is arbitrary. Alternatively, note $ a^2 - b^2 = (a - b)(a + b) $, and $ a^2 + b^2 = (a + b)^2 - 2ab $. This seems stuck. Instead, observe that $ S = rac{2(a^2 + b^2)}{a^2 - b^2} $. Let $ a = 1 $, $ b = i $: $ S = 0 $. Let $ a = 1 $, $ b = e^{i\pi/2} = i $: same. Let $ a = 1 $, $ b = -i $: same. But try $ a = 1 $, $ b = i $: $ S = 0 $. Let $ a = 2 $, but $ |a| = 1 $. No. Thus, $ S $ can vary. But the answer is likely $ S = 0 $, based on $ a = 1 $, $ b = i $. Alternatively, the expression simplifies to $ S = rac{2(a^2 + b^2)}{a^2 - b^2} $. However, for $ |a| = |b| = 1 $, $ a^2 \overline{a}^2 = 1 \Rightarrow a^2 = rac{1}{\overline{a}^2} $, but this doesn't directly help. Given $ a 📰 Roblox Free To Play No Download 865734 📰 Home Dwpot 1127931 📰 The Ultimate Lust Fma Experience Why This Content Arrests Every Viewer 4543874 📰 Step Into The Purple Aesthetic Ethereal Spaces That Will Captivate You 5039680 📰 Discover The Coolest Free Games You Havent Seen Yetplay Now 1677517 📰 See The Graphic Shock When You Spot The Minutes Level Differences In These Imagesinside 6660272 📰 What Is The Current Inflation Rate In The Us 📰 Tri Tip Rub The Secret Technique Guaranteed To Make Your Steak Rock 3532709 📰 Tata Iron And Steel Company Share Price 📰 Best Airport Clubs 📰 Redrock Canyon Grill 7079707 📰 Blue Cross Blue Shield Settlement 9974246 📰 Bank Of America Wyoming Mi 9507562 📰 No One Should Live Without This Step By Step Guide To Finding The Best Infrared Sauna Near You 9498784 📰 Echo And Narcissus 3613222