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Home » 236: The Jaw-Dropping Reason This Number Is Taking the Internet by Storm! - Network4

236: The Jaw-Dropping Reason This Number Is Taking the Internet by Storm! - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Verify solutions in the original equation to ensure no extraneous roots were introduced. Both values satisfy the equation.

📌 Question: Given three points on a topographic map—$ A(2, 5) $, $ B(7, 1) $, and $ C(3, 8) $—find the area of triangle $ ABC $ using coordinate geometry.

📌 Solution: Use the shoelace formula for the area of a triangle with vertices $ (x_1, y_1) $, $ (x_2, y_2) $, $ (x_3, y_3) $:

📌 Substitute $ A(2, 5) $, $ B(7, 1) $, $ C(3, 8) $:

📌 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 $:

📌 Set equal to zero for orthogonality:

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