Some conjectures on addition and multiplication of complex (real)   numbers
  We discuss conjectures related to the following two conjectures:   (1) for each complex numbers x_1,...,x_n there exist rationals y_1,...,y_n \in [-2^{n-1},2^{n-1}] such that   \forall i \in {1,...,n} (x_i=1 \Rightarrow y_i=1)   \forall i,j,k \in {1,...,n} (x_i+x_j=x_k \Rightarrow y_i+y_j=y_k)   (2) for each complex (real) numbers x_1,...,x_n there exist complex (real) numbers y_1,...,y_n such that   \forall i \in {1,...,n} |y_i| \leq 2^{2^{n-2}}   \forall i \in {1,...,n} (x_i=1 \Rightarrow y_i=1)   \forall i,j,k \in {1,...,n} (x_i+x_j=x_k \Rightarrow y_i+y_j=y_k)   \forall i,j,k \in {1,...,n} (x_i \cdot x_j=x_k \Rightarrow y_i \cdot y_j=y_k) 
Apoloniusz Tyszka