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Home » Break-even point: \( 2000 \div 20 = 100 \) units - Treasure Valley Movers

Break-even point: \( 2000 \div 20 = 100 \) units - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 A mathematician working on secure communication protocols analyzes a signal modeled by the complex function:

📌 \[ f(z) = z^2 + (1 + i)z + i \]

📌 Find all complex numbers \( z \) such that \( f(z) = 0 \).

📌 We solve the quadratic equation in complex numbers:

📌 \[ z^2 + (1 + i)z + i = 0 \]

📌 \[ z = \frac{-(1 + i) \pm \sqrt{(1 + i)^2 - 4(1)(i)}}{2} \]

📌 First, compute the discriminant:

📌 \[ (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i \]

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