A Möbius transformation is a function that maps the complex plane onto itself in a specific way, defined by the formula $$f(z) = \frac{az + b}{cz + d}$$, where $a$, $b$, $c$, and $d$ are complex numbers and $ad - bc \neq 0$. These transformations are essential in understanding the geometry of complex numbers and their functions, as they preserve angles and the general shape of figures.
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