767-300 - Anadea

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📅 May 14, 2026 👤 scraface

May 14, 2026

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767-300

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📰 Question: A quantum sensor measures two coherent signals represented by complex numbers $ z_1 = 1 + i $ and $ z_2 = a - i $, where $ a $ is a real parameter. Find $ a $ such that the signals are orthogonal in the complex plane. 📰 Solution: Two complex numbers $ z_1 = x_1 + y_1i $ and $ z_2 = x_2 + y_2i $ are orthogonal if their dot product $ x_1x_2 + y_1y_2 = 0 $. 📰 For $ z_1 = 1 + i $ and $ z_2 = a - i $: