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Home » r = 3, l = 5 → 15π ≈ 47.12 cm² - Veritas Home Health

r = 3, l = 5 → 15π ≈ 47.12 cm² - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Since all recorded values are accurate, total = 320 + 450 + 180 = 950.

📌 #### 950**Question:

📌 In a quantum computing model, if the probability amplitude for a qubit state is given by \( a + bi \) such that \( |a + bi| = 1 \), determine the values of \( a \) and \( b \) when the state represents a state with a phase difference of \( \frac{\pi}{3} \) from the real axis. Find the sum of all possible values of \( a \).

📌 Given that the probability amplitude \( a + bi \) lies on the unit circle, we have:

📌 \[ |a + bi| = \sqrt{a^2 + b^2} = 1 \Rightarrow a^2 + b^2 = 1. \]

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

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

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

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