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Home » After 2 hrs: \( 300 \times 1.5 = 450 \) - Crosslake

After 2 hrs: \( 300 \times 1.5 = 450 \) - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The work done by the field is:

📌 \boxed{18\pi}

📌 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}

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