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Home » In such problems, often expected: - Sourci

In such problems, often expected: - Sourci

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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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 \om...
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^...
= \sqrt{48\cos^2 \omega t + (\cos^2 \omega t + \sin^2 \omega t)} = \sq...
The maximum occurs when \( \cos^2 \omega t = 1 \):
|z(t)|_{\text{max}} = \sqrt{48 + 1} = \sqrt{49} = 7
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