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Home » Let the sides be \( a = 6 \) and \( b \). - Professionaloutdoormedia

Let the sides be \( a = 6 \) and \( b \). - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Question:** An electrical engineer studies a alternating current signal modeled by \( z(t) = 4e^{i\omega t} + 3e^{-i\omega t} \), where \( z(t) \) represents voltage in complex form. Compute the maximum real value of \( |z(t)| \).

📌 First, express \( z(t) \) in terms of cosine and sine:

📌 z(t) = 4(\cos \omega t + i\sin \omega t) + 3(\cos \omega t - i\sin \omega t) = (4 + 3)\cos \omega t + i(4 - 3)\sin \omega t

📌 z(t) = 7\cos \omega t + i\sin \omega t

📌 Now compute the magnitude:

📌 |z(t)| = \sqrt{(7\cos \omega t)^2 + (\sin \omega t)^2} = \sqrt{49\cos^2 \omega t + \sin^2 \omega t}

📌 = \sqrt{48\cos^2 \omega t + (\cos^2 \omega t + \sin^2 \omega t)} = \sqrt{48\cos^2 \omega t + 1}

📌 The maximum occurs when \( \cos^2 \omega t = 1 \):

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