The topic maybe not so rigor.

question1:

For example,here are four complex numbers.

B ={3/13 - (2 I)/13, 3/2 - (5 I)/2, -(7/2) - 13 I, 1 - 3 I}

List B can be easily manipulate like this in mathematica,

Re(B),Im(B)

In[31]:= Re[A]

Out[31]= {3/13,3/2,-(7/2),1}

In[32]:= Im[A]

Out[32]= {-(2/13),-(5/2),-13,-3}

and in maple,I creat the array like this:

n := (a, b, c, d)

a,b,c,d are the four elements corresponding to List B above.

A:=Array([a,b,c,d])