Abstract data types (ADTs) provide a way to define data structures and the operations allowed on them, independent of the specific implementation details. Choosing the appropriate data type is for many applications the most important step in their development that affects their performance. To investigate the most suitable stack implementation for evaluating arithmetic expressions with complex numbers, we developed an Android application. These expressions may contain a larger number of complex numbers, for example, 25, which can be enclosed in parentheses arbitrarily. The Android application uses an array and linked-list implementation of a stack ADT to evaluate these expressions in its methods, as well as a simple stack implementation that uses none ADT. We determined a more efficient implementation of a stack ADT and the most efficient implementation at all by analysing the execution times of these methods, which were evaluating the same arithmetic expressions with complex numbers. In the paper we also analyse the functioning of both these stack ADT implementations and a simple stack implementation that does not use an ADT.