Find the argument of

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Foundations of mathematical language · Foundations of mathematical language

Mathematical Methods for Physics, Ch Complex numbers, the complex exponential and phasors

Problem

Find the argument of z=−5−12iz = -5 - 12i. Someone computes: arg⁡z=tan⁡−1 ⁣(−12−5)=tan⁡−1(2.4)=1.176 rad,\arg z = \tan^{-1}\!\left(\frac{-12}{-5}\right) = \tan^{-1}(2.4) = 1.176\,\mathrm{rad}, and states this as the argument of zz. ((a)) Explain why this is wrong. ((b)) Give the correct value of arg⁡z\arg z (with −π<arg⁡z≤π-\pi<\arg z\le\pi) and the modulus ∣z∣|z|.

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