  Resource theory of imaginarity provides a useful framework to understand the
role of complex numbers, which are essential in the formulation of quantum
mechanics, in a mathematically rigorous way. In the first part of this article,
we study the properties of ``real'' (quantum) operations both in single-party
and bipartite settings. As a consequence, we provide necessary and sufficient
conditions for state transformations under real operations and show the
existence of ``real entanglement'' monotones. In the second part of this
article, we focus on the problem of single copy state transformation via real
quantum operations. When starting from pure initial states, we completely solve
this problem by finding an analytical expression for the optimal fidelity of
transformation, for a given probability of transformation and vice versa.
Moreover, for state transformations involving arbitrary initial states and pure
final states, we provide a semidefinite program to compute the optimal
achievable fidelity, for a given probability of transformation.
