I'm trying to sketch the nyquist plot of(adsbygoogle = window.adsbygoogle || []).push({});

$$\frac{j\omega-1}{j\omega+1}$$

but can't seem to calculate the argument correctly. I think it should be $$\arctan(-\omega) - \arctan(\omega) = -2\arctan(\omega)$$ but this doesn't give the correct nyquist plot behaviour for $\omega \to 0$ and $\omega \to \infty$ - surely $-2\arctan(\omega)$ implies that $\lim_{x\to 0} = 0^\circ$ and $\lim_{x\to \infty} = -180^\circ$?

Wolfram Alpha disagrees but I can't see where I'm going wrong. Am I making a glaring error somewhere? Any help would be greatly appreciated.

Thanks very much

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# Complex arguments

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