@misc{Maciuk_Arkadiusz_Vortices_2015,
 author={Maciuk, Arkadiusz and Smoluk, Antoni},
 identifier={DOI: 10.15611/me.2015.11.07},
 year={2015},
 rights={Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy},
 publisher={Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu},
 description={Mathematical Economics, 2015, Nr 11 (18), s. 77-88},
 language={eng},
 abstract={The paper emphasizes that complex numbers are objects with their equivalents commonly occurring in nature. Just like real numbers measure lengths in a physical world, complex numbers measure vortices observed in nature. The spiral orbits in this paper are exponential spirals (also called logarithmic spirals). A vortex is identified by determining a complex number that generates it. To determine this number, we need two snap-reading observations that provide the argument of a complex number, while the ratio of radiuses – the modulus of a complex number. Therefore, we also deal with the area of a complex number. Complex numbers involve a meaningful description of the laws of nature, i.e. of vortices and of equilibrium.},
 title={Vortices and complex numbers},
 type={artykuł},
 keywords={complex number, vortex},
}