  We investigate active galactic nuclei (AGN) candidates within the FourStar
Galaxy Evolution Survey (ZFOURGE) to determine the impact they have on
star-formation in their host galaxies. We first identify a population of radio,
X-ray, and infrared-selected AGN by cross-matching the deep $K_{s}$-band
imaging of ZFOURGE with overlapping multi-wavelength data. From this, we
construct a mass-complete (log(M$_{*}$/M$_{\odot}$) $\ge$ 9.75), AGN luminosity
limited sample of 235 AGN hosts over z = 0.2 - 3.2. We compare the rest-frame U
- V versus V - J (UVJ) colours and specific star-formation rates (sSFRs) of the
AGN hosts to a mass-matched control sample of inactive (non-AGN) galaxies. UVJ
diagnostics reveal AGN tend to be hosted in a lower fraction of quiescent
galaxies and a higher fraction of dusty galaxies than the control sample. Using
160{\mu}m Herschel PACS data, we find the mean specific star-formation rate of
AGN hosts to be elevated by 0.34$\pm$0.07 dex with respect to the control
sample across all redshifts. This offset is primarily driven by
infrared-selected AGN, where the mean sSFR is found to be elevated by as much
as a factor of ~5. The remaining population, comprised predominantly of X-ray
AGN hosts, is found mostly consistent with inactive galaxies, exhibiting only a
marginal elevation. We discuss scenarios that may explain these findings and
postulate that AGN are less likely to be a dominant mechanism for moderating
galaxy growth via quenching than has previously been suggested.
