> > q[1]:=3; q[1] := 3 > q[2]:=10; q[2] := 10 > n:=2; n := 2 > com:=(x,y)->x+I*y; com := (x, y) -> x + I y > com(1,2); 1 + 2 I > z[1]:=com(1,1); z[1] := 1 + I > z[2]:=com(3,2); z[2] := 3 + 2 I > contourplot(Re(log(com(x,y)-z[1])),x=0..4,y=0..4,grid=[70,70]); > phi := (z) -> sum(q[i]*log(z-z[i]), i=1..n); n ----- \ phi := z -> ) q[i] log(z - z[i]) / ----- i = 1 > > phi(com(1,0)); 3 ln(1 - 1[1]) + 10 ln(1 - 1[2]) > n; 2 > phi := (u) -> sum(q[i]*log(u-z[i]), i=1..n); n ----- \ phi := u -> ) q[i] log(u - z[i]) / ----- i = 1 > phi(com(1,0)); - 3/2 I Pi + 10 ln(-2 - 2 I) > contourplot(Re(phi(com(x,y))),x=0..4,y=0..4); > q[1]:=10; q[1] := 10 > contourplot(Re(phi(com(x,y))),x=0..4,y=0..4); > contourplot(Re(phi(com(x,y))),x=0..4,y=0..4,grid=[50,50]); >