Graphical interpretation of complex roots

Graphical interpretation of the complex roots of a quadratic equation.
Inspired by this post and this paper.

Edit and compile if you like:

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% Author: Izaak Neutelings (April 2022)
% Inspiration:
%  https://math.stackexchange.com/questions/401745/help-understanding-complex-roots
%  https://doi.org/10.5539/jmr.v10n6p91
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usepackage{physics}
\usepackage[outline]{contour} % glow around text
\contourlength{1.0pt}
\usetikzlibrary{3d}
\tikzset{>=latex} % for LaTeX arrow head
\usepackage{xcolor}
\colorlet{myblue}{blue!75!black}
\colorlet{mydarkblue}{blue!50!black}
\colorlet{myred}{red!65!black}
\colorlet{mydarkred}{red!40!black}
\tikzstyle{xline}=[myblue,very thick]
\tikzstyle{round xline}=[xline,line cap=round]
\tikzstyle{area}=[xline,fill=myblue!20,fill opacity=0.5]
\tikzstyle{yzp}=[canvas is zy plane at x=0]
\tikzstyle{xzp}=[canvas is xz plane at y=0]
\tikzstyle{xyp}=[canvas is xy plane at z=0]
\def\tick#1#2{\draw[thick] (#1) ++ (#2:0.11) --++ (#2-180:0.22)}
\def\N{50}
\begin{document}
% ONE REAL solutions
\begin{tikzpicture}[scale=1]
  \message{^^JReal solutions}
  \def\xmin{-0.4} % x axis minimum
  \def\xmax{3.8}  % x axis maximum
  \def\ymin{-0.4} % y axis minimum
  \def\ymax{2.7}  % y axis maximum
  \def\tmax{1.85} % parameter t maximum (upper)
  \def\A{0.7}     % parabola amplitude
  \def\a{1.75}    % parabola minimum
 
 
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