  A complex unit gain graph ($ \mathbb{T} $-gain graph), $ \Phi=(G, \varphi) $
is a graph where the function $ \varphi $ assigns a unit complex number to each
orientation of an edge of $ G $, and its inverse is assigned to the opposite
orientation. %A complex unit gain graph($ \mathbb{T} $-gain graph) is a simple
graph where each orientation of an edge is given a complex unit, and its
inverse is assigned to the opposite orientation of the edge. In this article,
we propose gain distance matrices for $ \mathbb{T} $-gain graphs. These notions
generalize the corresponding known concepts of distance matrices and signed
distance matrices. Shahul K. Hameed et al. introduced signed distance matrices
and developed their properties. Motivated by their work, we establish several
spectral properties, including some equivalences between balanced $ \mathbb{T}
$-gain graphs and gain distance matrices. Furthermore, we introduce the notion
of positively weighted $ \mathbb{T} $-gain graphs and study some of their
properties. Using these properties, Acharya's and Stani\'c's spectral criteria
for balance are deduced. Moreover, the notions of order independence and
distance compatibility are studied. Besides, we obtain some characterizations
for distance compatibility.
