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📰 $ u = rac{-64 \pm \sqrt{4096 + 576}}{2} = rac{-64 \pm \sqrt{4672}}{2} $. Not real? Wait, $ \sqrt{4672} = \sqrt{16 \cdot 292} = 4\sqrt{292} = 4\sqrt{4 \cdot 73} = 8\sqrt{73} $. So $ u = rac{-64 \pm 8\sqrt{73}}{2} = -32 \pm 4\sqrt{73} $. Take positive root: $ a^2 = -32 + 4\sqrt{73} $, messy. Instead, accept that $ |z|^2 + |w|^2 = |z + w|^2 + |z - w|^2 - 2|z \overline{w}| $, but no. Final correct approach: $ |z|^2 + |w|^2 = (z + w)(\overline{z} + \overline{w}) - 2 ext{Re}(z \overline{w}) = |z + w|^2 - 2 ext{Re}(z \overline{w}) $. But $ z \overline{w} + \overline{z} w = 2 ext{Re}(z \overline{w}) $. Also, $ (z + w)(\overline{z} + \overline{w}) = |z|^2 + |w|^2 + z \overline{w} + \overline{z} w = S + 2 ext{Re}(z \overline{w}) $. From $ z + w = 2 + 4i $, $ zw = 13 - 2i $, consider $ |z + w|^2 = 20 $, $ |zw|^2 = 173 $. Use identity: $ |z|^2 + |w|^2 = \sqrt{ |z + w|^4 + |z - w|^2 |z + w|^2 - 2|z|^2 |w|^2 } $ — too complex. Given time, assume a simpler path: From $ z + w = 2 + 4i $, $ zw = 13 - 2i $, compute $ |z|^2 + |w|^2 = |z + w|^2 + |z - w|^2 - 2|z \overline{w}| $. Not working. Use $ |z|^2 + |w|^2 = (z + w)(\overline{z} + \overline{w}) - 2 ext{Re}(z \overline{w}) = 20 - 2 ext{Re}(z \overline{w}) $. Now, $ z \overline{w} + \overline{z} w = 2 ext{Re}(z \overline{w}) $. Let $ S = |z|^2 + |w|^2 $, $ P = |z|^2 |w|^2 = 173 $. Also, $ (z + w)(\overline{z} + \overline{w}) = S + z \overline{w} + \overline{z} w 📰 Michael Rooker’s Hidden Movie Secrets You’ll Never Believe Revealed! 📰 Michael Rooker Films & TV Shows: The Shocking Truth Behind His Beloved Roles! 📰 The Shocking Truth Your Company Needs An Incident Response Planheres What Happens When You Dont 2617568 📰 Ghost Riley Exposed Why This Phantom Is Haunting Social Media Forever 9067111 📰 Martin House Brewery 478369 📰 Crazi Game The Hidden Rule Thatll Make You Laugh Shout And Quit Playing 7394321 📰 This Is Why Investors Are Rushinghow Qatar Airways Stock Is Setting Trends In 2024 3775845 📰 Gianni Bini Exposes The Hidden Truth That Shook His Familys Legacy 788664 📰 Sparkle Specialist 8158411 📰 Sql Server 2019 Get All User Permissions For Login 2407911 📰 The Hidden Hack To Perfect Soups Every Time Discover The Magic Of The Simmer Pot 8307953 📰 The Boys Season 5 Release Date 2314083 📰 Verizon Yonkers Cross County 4846755 📰 Wells Fargo Wells Fargo Wells Fargo 4780478 📰 Heels In Pink 2711486 📰 Whats The Highest Number 13 📰 Triangle Rectangle 1815231