M/E23

In 1965, Walter F. Penney proved that it is possible to represent every complex number using a ``binary`` system (that is, with digits 0 and 1) when we replace the radix 2 by the complex number -1+i. This inspired an extensive research about positional number systems in the complex plane. I will present an overview of results which are due to I. Kátai, J. Szabó, G. Steidl and others. In the second part of the talk, I will discuss analogical results which I obtained in the non-commutative field of quaternions.

Jakub Krasensky

Charles University, Prag