Stacking long short-term memory (LSTM) cells or gated recurrent units (GRUs) as part of a recurrent neural network (RNN) has become a standard approach to solving a number of tasks ranging from language modeling to text summarization. While LSTMs and GRUs were designed to model long-range dependencies more accurately than conventional RNNs, they nevertheless have problems copying or recalling information from the long distant past. Here, we derive a phase-coded representation of the memory state, Rotational Unit of Memory (RUM), which unifies the concepts of unitary learning and associative memory. We show experimentally that RNNs based on RUMs can solve basic sequential tasks such as memory copying and memory recall much better than LSTMs/GRUs. We further demonstrate that by replacing LSTM/GRU with RUM units we can apply neural networks to real-world problems such as language modeling and text summarization, yielding results comparable to the state of the art.