  Certain real parameters of a Hamiltonian, when continued to complex values,
can give rise to singular points called exceptional points ($EP$'s), where two
or more eigenvalues coincide and the complexified Hamiltonian becomes
non-diagonalizable. We show that for a generic $d$-dimensional topological
superconductor / superfluid with a chiral symmetry, one can find $EP$'s
associated with the chiral zero energy Majorana fermions bound to a topological
defect / edge. Exploiting the chiral symmetry, we propose a formula for
counting the number ($n$) of such chiral zero modes. We also establish the
connection of these solutions to the Majorana fermion wavefunctions in the
position space. The imaginary parts of these momenta are related to the
exponential decay of the wavefunctions localized at the defect / edge, and
hence their changes of signs at a topological phase transition point signal the
appearance or disappearance of chiral Majorana zero modes. Our analysis thus
explains why topological invariants like the winding number, defined for the
corresponding Hamiltonian in the momentum space for a defectless system with
periodic boundary conditions, capture the number of admissible Majorana fermion
solutions for the position space Hamiltonian with defect(s). Finally, we
conclude that $EP$'s cannot be associated with the Majorana fermion
wavefunctions for systems with no chiral symmetry, although one can use our
formula for counting $n$, using complex $k$ solutions where the determinant of
the corresponding BdG Hamiltonian vanishes.
