OFDM allows us to do this the "easy way"! Notice that each carrier is simply a bin in the FFT (if we were to take an FFT of the combined result). So with OFDM we simply start with that, load the constellation onto each bin according to our mapping and then take the inverse FFT to create the equivalent analog signal that the above would create (as a complex signal that we would need to translate to a real RF carrier at an IF or RF frequency). There is a lot more detail with OFDM such as adding a cyclic prefixes to avoid the effects of delay spread that I am not mentioning here, but the intention with this introduction is to remove the mystery of how the complex signals for each DFT bin can represent the equivalent analog waveform to a multi-carrier QPSK/QAM system. Further the above shows the most generic form fully utilizing the independent bins in a full FFT, but OFDM implementations can also be done with Hermitian symmetry ($N/2+k = k^*$) such that the direct output can be real such that and IQ frequency translation is not required.
The complete OFDM transmitter as is shown below in its typical form, where we see this is an equivalent structure to what was developed above and the importance of the complex values for each QPSK/QAM symbol as represented by $k_0$, $k_1$, etc.
If the frequency translation with complex signals as depicted in this post is still not clear, the follow post may also be helpful and get to root of the OP's question that goes far beyond OFDM specifics: