This book includes a wide range of topics from basic foundations to advanced applications. Different chapters may be suitable for special groups. Part I is useful for the levels of researchers and graduate students. Conjugate complex vector operators, symmetry/anti-symmetry brackets, Lie-Dirac-conjugate algebra, conjugate combinatorial lattices are suitable for basic researchers on logic, probability, statistics, complex foundation, parallel synchronous time orders/modeling/analysis, complex analysis, complex geometric foundation, measures on mathematical foundation, combinatorial mathematics, meta-mathematics, quantum logic, and combinatorial group theory. Part II is useful for the general audience on history development of complex conjugate numbers and quantum entanglement paradoxes. Richer visual maps of entangled experimental and simulated results are valuable for application researchers and engineers, senior college students and postgraduate students in quantum information, quantum communication, quantum computing, quantum computers. The future applications are suitable for general researchers, engineers, postgraduate, and senior undergraduate students.