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.

Fri, 17 Apr 2026 08:40:38 +0000

**How Quantum Sensors Use Complex Signal Orthogonality—And Why It Matters** In today’s rapidly advancing tech landscape, quantum sensors are capturing headlines as tools poised to revolutionize precision measurement across medicine, navigation, and communications. At the heart of this innovation lies a fundamental mathematical principle: signal orthogonality. When two signals are orthogonal in the complex plane, their interaction—when processed through sensitive quantum systems—reveals maximum insight without interference. This concept grows increasingly relevant as researchers explore real-world quantum applications. But what does it mean for signals represented by complex numbers, and how do parameters like $ a $ shape their behavior? --- **Why Signal Orthogonality Is a Hot Topic Now**