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Results tagged with complex-numbers
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user 1684451
Questions involving complex numbers, that is numbers of the form $a+bi$ where $i^2=-1$ and $a,b\in\mathbb{R}$.
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Determining the regions of the z-plane for $|\frac{z+a}{1+\bar{a}z}|<1,|\frac{z+a}{1+\bar{a}...
Try studying the equation
$$
(|z|^{2} - 1)(|a|^{2} - 1) = 0
$$
for given cases on $|\bar{a}|$.
If $|\bar{a}| \neq 1$, then we have
$$
(|z|^{2} - 1)(|a|^{2} - 1) = 0\Longrightarrow|z^{2}| = 1
$$
which …
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