I want to plot the complex numbers

(-1/2)^q+(-1/2)^(1-q)  (0.25<=q<=0.5)

on the complex plane. Does exist a package (some commands) which can do it?

Sandor

I use Optimization package and I obtain a warning

"Warning, no iterations performed as initial point satisfies first-order conditions"

What is the first-order condition?

Thanks,    Sandor

dsolve(diff(r(t),t$1)=-r(t)*(-1+r(t)^2));

                       1                                  1           
     r(t) = ------------------------, r(t) = - ------------------------

I have an  ode system, and use  2 D Math  (I don't know how to copy here, so I type by hand)

x'(t) = -y(t) + x(t) (1 - x^2(t)  -  y^2(t)),

y'(t) = x(t) + y(t) (1 - x^2(t) - y^2(t)).

I would like to introduce  x(t) = r(t) cos(Theta(t)), y(t) = r(t) sin(Theta(t)) and manipulate the equations further.

The problem is the left hand side. In one case I obtain Dx(t), in the other case (r(t) cos(Theta(t))' without calculation on it.

I ask some help. Thanks.

I have a matrix (made by Matrix palette)

> LapMatrix := Matrix(3, 3, {(1, 1) = 1/sin(Theta)^2, (1, 2) = -cos(Theta), (1, 3) = 0, (2, 1) = -cos(Theta), (2, 2) = 1/sin(Theta)^2, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1});

Maple calculated the 3 eigenvalues.

When I typed

(v,e):=Eigenvectors(LapMatrix)

Maple said

Error, (in LinearAlgebra:-LA_Main:-Eigenvectors) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values