  We report first study of complex field inflation. Although understood as a
specific two-field inflation, a complex field inflation is able to make more
robust model predictions on primordial curvature perturbation. Explicitly we
discuss the model realizations of complex chaotic and exponential inflation in
various large-field contexts. Both complex field models contain a single
complex scalar together with only two free parameters. Using numerical handles
aimed to calculate primordial curvature perturbation from multifield inflation,
we show that both models are compatible with current Planck data, and the
individual surviving parameter space can be substantially or fully probed by
future CMB-S4 experiments.
