restart;
z1:=2+3*I:
z2:=I:
op(z1);
op(z2);

                                                                         2, 3
                                                                          1

A reliable way to iterate over the sum of multiple terms is to simply make those terms elements of a list.

restart:
with(plottools): with(plots):
u:=[2,2]: v:=[2,-1]:
G1:=seq(line(-5*u+t*v,5*u+t*v,linestyle=2), t=-5..5):
G2:=seq(line(s*u-5*v,s*u+5*v,linestyle=2), s=-5..5):
U:=arrow(u, color=red, width=0.2):
V:=arrow(v, color=red, width=0.2):
plots:-display(U,V,G1,G2, size=[700,700], scaling=constrained, axes=none);
    

We have to use the  parametric  option:

restart;
solve({-x1+2*x2+(2-p)*x3=0,(2-p)*x2+x3=2, (1-p)*x1+2*x2+2*x3=p+3}, {x1,x2,x3}, parametric=true):
value(%);

Your syntax is correct and works successfully, but the following small improvements can be made:

1. The inequality  y>-1  can be omitted, since your region is itself above the line  y=-1 .
2. The  optionsexcluded = (color = white)  option can also be omitted, as it is done by default.
3. I equalized the ranges along the axes and shortened them a bit. With equal ranges, all shapes are unchanged and the  scaling=constrained  option is not required.

restart: with(plots):
inequal({y >= x^2+1, (x-1)^2+(y-1)^2 <= 16}, x = -3.5 .. 5.5, y = -3.5 .. 5.5, optionsfeasible = (color = grey));

The  solve  command is not intended for solving matrix equations. You can solve your problem using a simple for-loop. Note that to check for matrix equality, we must use the  LinearAlgebra:-Equal command:

Download Mapleprimes_Question_Book_2_Paragraph_4.1_Question_9_new.mw

Use the  factor  command for this:

factor(f);

                    A*sin(x)*theta(x)*(-m*omega^2+k)

By default, Maple calculates with 10 significant digits. Therefore, for a sufficiently large  x  of float type, we get ln(x+1) - ln(x) = 0. . If we increase the accuracy of the calculations, then the error disappears:

restart;
f := x->4*x*(ln(x+1)-ln(x)):
Digits := 50: 
evalf[10]~([seq(f(10.^n), n = 1 .. 10)]);

  [3.812407192, 3.980132341, 3.998001332, 3.999800013, 3.999980000, 3.999998000, 3.999999800, 3.999999980, 3.999999998, 4.000000000]

We can simply calculate this determinant and, equating it to  0 , we get a 4th degree equation for  w  with 2 parameters  d  and  k . Giving some values to these parameters, we find all values of  w . In the example below we find the real  d=2, k=1, w=sqrt(3)/3  for which  the determinant  is  0 :

Download det_new.mw

restart;
with(Student[Calculus1]):
soln := Roots(y-0.4646295e-3*tanh(y)+0.1839145082e-2*tanh(y)/(0.6000000000e-3*y^2-0.1840000000e-2), y);
map(t->t*I, soln);

p := 8*T(x, 7)*T(x, 2)+4*T(x, 5)*T(x, 1)+6*T(x, 3)*T(x, 3)+7*T(x, 1)*T(x, 4):
map(t->content(t)*`if`(type(primpart(t),`*`),convert(primpart(t),`+`),op(1,primpart(t))*op(2,primpart(t))), p);

                              8*T(x, 7)+8*T(x, 2)+4*T(x, 5)+11*T(x, 1)+12*T(x, 3)+7*T(x, 4)

Here is an another simple way (without select):

{seq(`if`(a>=5 and a<=15,a,NULL),a=A)};

move all terms to the left and take the numerator of the resulting fraction. In this case, the  expand  command is not required:

van_der_Waals := (p + a / V[m]^2) * (V[m] - b) = R * T:
numer((lhs-rhs)(van_der_Waals));
sort(%, V[m]);

restart;
Expr:=-a2/3 + a3 - (2*a4)/3 - (2*a5)/3:
Expr1:=-``(-Expr*3)/3; # The desired form
expand(Expr1); # The original form

Use functional notation:

Download CD_new.mw

2 errors in your code. In the EqBIS procedure, P, U, V must be Vectors, not lists. Also remove the space after the procedure name in your example (which Maple interprets as a multiplication sign). I also removed the unnecessary command RETURN:

EqBIS := proc(P, U, V)
local a, eq1, M1, t, PU, PV, bissec1;
a := (P - U)/LinearAlgebra:-Norm(P - U, 2) + (P - V)/LinearAlgebra:-Norm(P - V, 2);
M1 := P + a*t;
eq1 := op(eliminate({x = M1[1], y = M1[2]}, t));
op(eq1[2]); end proc;

EqBIS(<4, 5>, <11, 7/3>, <11, 5>);