Coherent detection requires exact knowledge of the channel state information, which is often a challenging task in demanding practical applications. Based on this, non-coherent detection of differentially modulated signals can be considered as an alternative method. The present paper investigates the effects of in-phase/quadrature-phase imbalance (IQI), which are known to degrade the performance of wireless communication systems. Specifically, we evaluate the effects of IQI on the bit error rate (BER) performance of differential quadrature phase shift keying (DQPSK) for ideal receiver (RX) with transmitter (TX) IQI, ideal TX with RX IQI and joint TX/RX IQI. Explicit analytic expressions are derived for the BER of both single-carrier and multi-carrier systems suffering from IQI at the TX and/or RX. Extensive Monte-Carlo simulation as well as offered analytic results show that realistic TX/RX IQI values can degrade the corresponding BER by over 30%. Likewise, it is shown that the detrimental effects of IQI are more considerable on DQPSK than on QPSK.