  We propose a simple method of combined synchronous modulations to generate
the analytically exact solutions for a parity-time symmetric two-level system.
Such exact solutions are expressible in terms of simple elementary functions
and helpful for illuminating some generalizations of appealing concepts
originating in the Hermitian system. Some intriguing physical phenomena, such
as stabilization of a non-Hermitian system by periodic driving, non-Hermitian
analogs of coherent destruction of tunneling (CDT) and complete population
inversion (CPI), are demonstrated analytically and confirmed numerically. In
addition, by using these exact solutions we derive a pulse area theorem for
such non-Hermitian CPI in the parity-time symmetric two-level system. Our
results may provide an additional possibility for pulse manipulation and
coherent control of the parity-time symmetric two-level system.
