Reconstruction of BandPass Signal from Complex Envelope
Let’s get one thing straight. You cannot recover the original real and imaginary parts of a complex signal based only on the magnitude values of the complex signal. That’s equivalent to saying, “I have the magnitude of a complex number. How do I compute that complex number’s real and imaginary parts?” There are an infinite number of possible correct answers to that question!

However, as MBaz rightly said, you don’t have any “envelope” signal in your block diagrams. And by the way, there are no such things as “complex envelope” signals. All “envelope” signals are real-only. Having said all of that, you can learn everything about your two block diagrams by writing down the algebraic equations for all their various signals. (Your textbook should have done that for you.) Then pay attention to all the various trigonometric identities in your math reference book. It’s a mild pain to do all of that, but it’s terrifically educational.

And another thing, your two block diagrams are not the normal “complex modulator” and “complex demodulator” used in modern digital communications systems. In a normal digital comms system the real-valued gI(t)/2 and gQ(t)/2 would be added (or subtracted, I forget) to produce a new real-valued signal that’s transmitted via an antenna. Have a look at Figure 1 of the following PDF file: http://www.testequity.com/documents/pdf/keysight/complex-modulation-generation-wp.pdf