By combining the functions of a poly phase filter and a variable gain amplifier, a 2nd order active complex filter is proposed in this paper for 5G and other broadband applications. Thanks to the TIA based structure, the complex filter has an operating speed up to 2.3GHz and a variable voltage gain of 0-20dB. Its center frequency is programmable from 500MHz to 1.85GHz by integrating an on-chip capacitor tank. An image rejection ratio of higher than 17dB is achieved when its gain is 14dB for all center frequency settings, consuming less than 40.6mW from a 1.4V supply. Fabricated in a 65nm CMOS process, the core circuit area is 0.25mm×0.2mm. To the best knowledge of the authors, this work is the first published GHz active complex filter, advancing the state-of-the-art.