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📰 Question: Let $ p $ and $ q $ be complex numbers such that $ p + q = 3 + 4i $ and $ p^2 + q^2 = 10 - 24i $. Find $ pq $. 📰 Solution: Use identity $ p^2 + q^2 = (p + q)^2 - 2pq $. Substituting: $ 10 - 24i = (3 + 4i)^2 - 2pq $. Compute $ (3 + 4i)^2 = 9 + 24i - 16 = -7 + 24i $. Then $ 10 - 24i = -7 + 24i - 2pq $. Rearranging: $ 17 - 48i = -2pq \Rightarrow pq = \frac{-17 + 48i}{2} $. \boxed{-\dfrac{17}{2} + 24i} 📰 Question: For all real numbers $ x $, find the number of functions $ f: \mathbb{R} \to \mathbb{R} $ satisfying $ f(x + y) = f(x) + f(y) + 2xy $. 📰 Go Pure Neck Cream 8998105 📰 Organ Trade 2244350 📰 Upgrade To These Huge Cat Furniture Piecesyour Job Just Got Easier With Cats 7730883 📰 These Zombie Games Are Crazyprepare For Brainfreeze And Heart Pounding Thrills 6052 📰 Studio 60 On The Sunset Strip 527574 📰 Unleash The Thrill Top Game Motorbike Games That Will Dominate Your Gaming Lifestyle 1554725 📰 How Many Mils In One Litre 5511395 📰 Caught The Biggest Rare Caught In Raidsno One Knows How It Worked 6452946 📰 Kaley Cuocos Nudes Go Public Is This The Most Watched Celebrity Sext Scene Ever 7868600 📰 Act Your Ps3 Into The Ps5 Erathis Secret Method Will Change Everything 5822702 📰 Why Every Man Needs High Quality Mens Linen Pants In 2024 5581464 📰 Java Chip Frappuccino The Secret Ingredient Making Coffee Lovers Crave More 7262639 📰 Amore E Amore 5534353 📰 Englsh To Spanish 5544701 📰 Hotel Reverie Review 4322910