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Home » The All-New Gear 5: Fixing Gears 1–4 AND Delivering Epic Performance! - 500apps

The All-New Gear 5: Fixing Gears 1–4 AND Delivering Epic Performance! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A phase difference of \( \frac{\pi}{3} \) from the real axis means the complex number is:

📌 \[ a + bi = \cos\left(\frac{\pi}{3}\right) + i\sin\left(\frac{\pi}{3}\right). \]

📌 \[ \cos\left(\frac{\pi}{3}\right) = \frac{1}{2}, \quad \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}. \]

📌 \[ a = \frac{1}{2}, \quad b = \frac{\sqrt{3}}{2}. \]

📌 Since the phase is fixed and the amplitude is normalized, the only possible real part is \( a = \frac{1}{2} \). There are no other values satisfying both the magnitude and phase condition.

📌 Therefore, the sum of all possible values of \( a \) is simply:

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