Thanks for the detailed answer and for your time.
please do me one more favour, that in
In[30]:= v = Total[{exp1, exp2, exp3, exp4} /. Equal[l_, r_] -> Norm[l - (r)]];
NMinimize[v, {x1, y1, x2, y2}, MaxIterations -> 10^3]
Out[31]= {6.92979*10^-15, {x1 -> -0.981789, y1 -> 0.163141, x2 -> 1.06868, y2 -> 0.614297}}
suggest me another command so that i get all possible 4 values of each variable, not only the one, although this is good approximation. But in my case in all above values of variables only one is the zero of a special function, for which i should have f(x1+i y1)=0, and f(x2+i y2)=0
But with the above value i am not getting good approximation .
I mean as you can see in
In[27]:= NSolve[{exp1, exp2, exp3, exp4}, {x1, y1, x2, y2}, Reals]
Out[27]= {{x1 -> -1.08337, y1 -> 0.622023, x2 -> 1.08337, y2 -> 0.622023},
{x1 -> -0.981789, y1 -> 0.163141, x2 -> 1.06868, y2 -> 0.614297},
Is the one we got by your command but with this f()=0.1(-01)
{x1 -> 1.06868, y1 -> 0.614297, x2 -> -0.981789, y2 -> 0.163141},
{x1 -> 1.08337, y1 -> 0.622023, x2 -> -1.08337, y2 -> 0.622023}}
But I need this last one as this gives f(x1+iy1)=1.2(-13),and f(x2+i y2)=3.5(-12) accuracy