This paper deals with a kind of synchronization of dynamical systems with complex variables which is
called generalized complex modified hybrid function projective synchronization (GCMHFPS) of time delay
complex chaotic (hyperchaotic) systems. In other words, that the time delay complex systems can
be synchronized up to a complex function transformation matrix. Moreover, the elements of the transformation
matrix are complex functions of the states of drive system and time, where this matrix is not
square. The idea of an active control method based on complex Krasovskii–Lyapunov functional is used to
achieve GCMHFPS of time delay complex systems. Furthermore, based on the non-diagonal complex function
transformation matrix, the modules and phases errors between one state of the complex response
system and more than one of the states of the drive system are studied which have not been discussed
before as far as we know. The analytical expression regarding the stability of this technique is derived
and excellent agreement is found upon comparison with numerical calculations. In particular, we show
through studying the time evolution of error, modulus and phase that the proposed scheme is effective
for controlling time delay complex systems.