  In previous papers, we discussed the recurrence relations of the
multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson,
Askey-Wilson, Racah and $q$-Racah types. In this paper we explore those of the
Meixner-Pollaczek and continuous Hahn types. For the $M$-indexed
Meixner-Pollaczek and continuous Hahn polynomials, we present $3+2M$ term
recurrence relations with variable dependent coefficients and $1+2L$ term
($L\geq M+1$) recurrence relations with constant coefficients. Based on the
latter, the generalized closure relations and the creation/annihilation
operators of the quantum mechanical systems described by the multi-indexed
Meixner-Pollaczek and continuous Hahn polynomials are obtained.
