I've uploaded an image showing a demonstration I'd like to create, but I definitely need help. There is a lot of talent on this list, so maybe someone can help me get started learning how to add graphics to a plot and animate them.
What I'd like to create is a
Manipulate demonstration that will animate the plot of
Exp[I θ] + b Exp[-I θ], where
b is a real number between 0 and 1. As you can see in the attached figure, I want to draw two circles centered at the origin, one with radius 1, the second with radius
b. I'd like the
Manipulate to have a slider that will allow me to vary the value of
b between 0 and 1.
Next, I want to draw the vectors
Exp[I θ] and the vector
b Exp[-I θ], as pictured in the sketch. Then I want to complete the parallelogram and draw the vector
Exp[I θ] + b Exp[-I θ]. I also want a slider for
θthat varies from 0 to 2 π, and when I move the slider, I want to see all of the vectors move, the parallelogram adjust, and the tip of the vector
Exp[I θ] + b Exp[-I θ] trace out the dotted ellipse.
I'd really appreciate it if someone could show me how to do this.
This was overlooked in the initial answers:
How do we add the curve
Exp[I θ] + b Exp[-I θ] to the figure?