In twin paradox, there is an unaccounted area in the unaccelerated frame of its Space-time diagram when one frame's simultaneity is being mapped to the other; ergo period motion of pendulum in one frame to another to reckon for time elapsing. This unaccounted area is due to the fact that time is intrinsically complex, what we observed in time in daily is real/complex part. If We invoke another 2nd order rotation perpendicular to original space-time diagram, which I presumably think it suggests that time is complex, the unaccounted area (in time elapsing) could presumably be resolved. Is this line of thought correct?
There is no indication that time is complex. There was some work in the early days of special relativity that treated time as purely imaginary.
However, that work has been largely discarded for nearly a century now. It never solved any theoretical problems, simplified any calculations, or made any new experimental predictions. Furthermore (and probably more importantly), that approach did not translate well to general relativity. So the Lorentzian metric signature approach was used instead, which does translate directly to general relativity. The Lorentzian metric signature approach addresses everything that the imaginary time approach addressed, but using real numbers and in a mathematically preferable way.