Updater Function with Complex Plane

[SuperUser-Vermeylen]

I want to display the complex coordinate next to a dot much like is observed in this example.

I can overlay the example with a complex plane but I can't get a complex dot to display its value.

class Complex_Dots_with_Labels(Scene):
    def construct(self):
        def d1_position(mobject):
            mobject.set_value(d1.get_center()[0])
            mobject.next_to(d1)

        def d2_position(mobject):
            mobject.set(value = '{0:.1f}{1}{2:.1f}i'.format(d2.get_center()[0],
                                                            '+-'[d2.get_center()[1] < 0],
                                                            d2.get_center()[1]))
            mobject.next_to(d1)
        
        initial_point = 1+1j
        
        plane = ComplexPlane().add_coordinates()
        
        d1 = Dot(RIGHT*3)
        d2 = Dot(plane.n2p(initial_point), color=YELLOW)
        
        l1 = DecimalNumber()
        l2 = MathTex()
        
        l1.add_updater(d1_position)
        l2.add_updater(d2_position)
        
        self.add(d1, d2, l1, l2, plane)

        self.play(Rotating(d1, about_point=ORIGIN, angle=TAU, run_time=TAU, rate_func=linear),
                  Rotating(d2, about_point=ORIGIN, angle=TAU, run_time=TAU, rate_func=linear))

I understand there exists a ComplexValueTracker, but I don't know how to use it.

How do I get a dot on the complex plane to display its cordinate as it traverses a path across the plane?

[SuperUser-Vermeylen]

Here is what I have so far:

class Complex_Dots_with_Labels(Scene):
    def construct(self):
        
        def label_value_and_position(mobject):
            position_string = "{} + {}".format(round(dot.get_center()[0], 2), round(dot.get_center()[1],2))
            mobject.set(submobjects = [SingleStringMathTex(position_string)])
            mobject.next_to(dot)
        
        tracker = ComplexValueTracker(-2+1j)
        dot = Dot(color = YELLOW).add_updater(lambda x: x.move_to(tracker.points))
        label = MathTex().add_updater(label_value_and_position) 
        
        self.add(ComplexPlane().add_coordinates(), dot, label)

        self.play(tracker.animate.set_value(3+2j))
        self.play(tracker.animate.set_value(tracker.get_value() * 0.5j))
        self.play(tracker.animate.set_value(tracker.get_value() - 4+2j))
        self.play(tracker.animate.set_value(tracker.get_value() / (-2 + 3j)))
        self.play(tracker.animate.set_value(-2+1j))

Some strange artifacts have popped up and it takes a while, about 10 seconds, to render.
I could use help with efficiency as well.

[SuperUser-Vermeylen]

Faster render and I'm approaching the desired outcome.

class Complex_Dots_with_Labels(Scene):
    def construct(self):
        
        def label_value_and_position(mobject):
            position_string = "{0:.1f}{1}{2:.1f}i".format(dot.get_center()[0],
                                                          '+-'[dot.get_center()[1] < 0],
                                                          dot.get_center()[1])
            mobject.set(submobjects = [SingleStringMathTex(position_string)])
            mobject.next_to(dot)
        
        tracker = ComplexValueTracker(-2+1j)
        tracker_string = "{0:.1f}{1}{2:.1f}i".format(tracker.points[0][0],
                                                     '+-'[tracker.points[0][1] < 0],
                                                     tracker.points[0][1])
        
        dot = Dot(color = YELLOW).add_updater(lambda x: x.move_to(tracker.points))
        label = MathTex(tracker_string).add_updater(label_value_and_position) 
        
        self.add(ComplexPlane().add_coordinates(), dot, label)

        self.play(tracker.animate.set_value(3+2j))
        self.play(tracker.animate.set_value(tracker.get_value() * 0.5j))
        self.play(tracker.animate.set_value(tracker.get_value() - 4+2j))
        self.play(tracker.animate.set_value(tracker.get_value() / (-2 + 3j)))
        self.play(tracker.animate.set_value(-2+1j))

It has the artifact of tracker points appearing before the label and dot make their way to the position indicated by the tracker points.

Complex_Dots_with_Labels.mp4

[SuperUser-Vermeylen]

Got it!

class Complex_Dots_with_Labels(Scene):
    def construct(self):
        def label_value_and_position(mobject):
            position_string = "{0:.1f}{1}{2:.1f}i".format(dot.get_center()[0],
                                                          '+-'[dot.get_center()[1] < 0],
                                                          abs(dot.get_center()[1]))
            mobject.set(submobjects = [SingleStringMathTex(position_string)])
            mobject.next_to(dot)
        
        tracker = ComplexValueTracker(2*np.exp(np.pi*1j))
        dot = Dot(color = YELLOW).add_updater(lambda x: x.move_to(tracker.points[0]))
        label = MathTex().add_updater(label_value_and_position)
        
        self.add(ComplexPlane().add_coordinates(), dot, label)
        self.play(Rotating(dot, about_point=ORIGIN, angle=TAU, run_time=TAU, rate_func=linear))

Complex_Dots_with_Labels.mp4