  We propose a class of general non-Hermitian quasiperiodic lattice models with
exponential hoppings and analytically determine the genuine complex mobility
edges by solving its dual counterpart exactly utilizing Avila's global theory.
Our analytical formula unveils that the complex mobility edges usually form a
loop structure in the complex energy plane. By shifting the eigenenergy a
constant $t$, the complex mobility edges of the family of models with different
hopping parameter $t$ can be described by a unified formula, formally
independent of $t$. By scanning the hopping parameter, we demonstrate the
existence of a type of intriguing flagellate-like spectra in complex energy
plane, in which the localized states and extended states are well separated by
the complex mobility edges. Our result provides a firm ground for understanding
the complex mobility edges in non-Hermitian quasiperiodic lattices.
