If z is a complex number such that |z - bar{z | vedclass

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Question

Let $z=x+i y \Rightarrow|z+\bar{z}|=4 \Rightarrow x=\pm 2$

$|z-\bar{z}|=2 \Rightarrow y=\pm 1$

If $\mathrm{Amp}(\mathrm{z})=	heta$ then $	an \

Vedclass · Accepted Answer

$Amp(z)\in(\frac{\pi}{6},\frac{\pi}{4})$

Vedclass · Answer

Let $z=x+i y \Rightarrow|z+\bar{z}|=4 \Rightarrow x=\pm 2$

$|z-\bar{z}|=2 \Rightarrow y=\pm 1$

If $\mathrm{Amp}(\mathrm{z})=	heta$ then $	an 	heta=\pm \frac{1}{2}$

$\Rightarrow 	heta \in\left(0, \frac{\pi}{6}ight),\left(-\frac{\pi}{6}, 0ight),\left(\frac{5 \pi}{6}, \piight),\left(-\pi, \frac{-5 \pi}{6}ight)$

If $z$ is a complex number such that $|z - \bar{z}| = 2$ and $|z + \bar{z}| = 4 $, then which of the following is always incorrect -

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