As the matter of fact with BPSK (Binary Phase Shift Keying) which characterized by the information carried by the transmitted wave is contained in the phase. Particularly, in QPSK, the phase of the carrier takes on one of the four equally spaced values, such as pi/4, 3pi/4, 5pi/4 and 7pi/4. In QPSK, complete bit stream is divided into even bits (in-phase i.e. I) and odd bits (Quadra-phase i.e. Q) which combined together to get QPSK signal
General Formula for QPSK can be considered as
b(t) = b_even(t)*cos (2*pi*fc*t) + b_odd(t)*sin (2*pi*fc*t)
NOTE : Magnitudes of the QPSK signal is not considered and signal is normalized.
Ref : S. Haykin, "Digital Communication", John Wiley & Sons Inc., 1988, pp. - 284-290