Fig. 1: Examples 1–8 (from applet) of Descartes' ovals are composed of sections of complex functions taken at specific intervals.
Fig. 2: Example 2 of Examples 1-8 of the applet under consideration is notable in that the functions f3(x) and f4(x) are not defined in the real domain.
Figures a–d show the complex functions g1(z)–g4(z). Note that the functions of the imaginary parts of the complex functions g3(z) and g4(z) do not have intervals on the x-axis where they are zero.
![[size=85][b]Fig. 1:[/b] [b] Examples 1–8 (from [url=https://www.geogebra.org/m/cgfbcxau]applet[/url]) of Descartes' ovals are composed of sections of complex functions taken at specific intervals.[/b][/size]](https://stage.geogebra.org/resource/ybxvjyvn/CNR5Dvins0cXGXlN/material-ybxvjyvn.png)
![[size=85] [b]Fig. 2: [/b] Example 2 of Examples 1-8 of the applet under consideration is notable in that the functions [b][color=#0000ff]f3(x)[/color][/b] and [color=#6aa84f][b]f4(x)[/b][/color] are not defined in the real domain.
Figures a–d show the complex functions [b][color=#f6b26b]g1(z)–g4(z)[/color][/b]. Note that the functions of the[color=#f6b26b] imaginary parts[/color] of the complex functions [b][color=#f6b26b]g3(z)[/color][/b] and [b][color=#f6b26b]g4(z)[/color][/b] do not have intervals on the x-axis where they are zero.[/size]](https://stage.geogebra.org/resource/xbnmery9/jNF1in7UxjFnSSw7/material-xbnmery9.png)