  We investigate the nature of quantum criticality and topological phase
transitions near the critical lines obtained for the extended Kitaev chain with
next nearest neighbor hopping parameters and non-Hermitian chemical potential.
We surprisingly find multiple gap-less points, the locations of which in the
momentum space can change along the critical line unlike the Hermitian
counterpart. The interesting simultaneous occurrences of vanishing and sign
flipping behavior by real and imaginary components, respectively of the lowest
excitation is observed near the topological phase transition. Introduction of
non- Hermitian factor leads to an isolated critical point instead of a critical
line and hence, reduced number of multi-critical points as compared to the
Hermitian case. The critical exponents obtained for the multi-critical and
critical points show a very distinct behavior from the Hermitian case.
