Elementary Functions of a Complex Variable

Abstract

In the preceding chapters we studied complex numbers from an algebraical point of view, coupled with geometrical interpretations, and this enabled us to arrive at a sensible and consistent definition of powers z ^r, where r is an integer. We also discussed fractional powers and their many-valuedness. Thus we are in the position to handle expressions like ${{\left( {{z^{\tfrac{1}{2}}} + 2{z^{ - 5}}} \right)} \mathord{\left/ {\vphantom {{\left( {{z^{\tfrac{1}{2}}} + 2{z^{ - 5}}} \right)} {\left( {3{z^2} + i} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {3{z^2} + i} \right)}}$, in which several such powers are combined.