Move label of an angle in Tikz
The text pic text has the option text pic options
. Here, simply move the text up to the left to avoid overlapping on the side z_1
of the angle.
pic text options={shift={(-3pt,3pt)}}
I took the liberty of colouring the different angles, which in my humble opinion makes the figure easier to read.
\documentclass{article}
\usepackage{tkz-euclide}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{subcaption}
\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}
\begin{tikzpicture}[scale=1]
\begin{scope}[thick,font=\scriptsize]
\draw [->] (-.5,0) -- (5.5,0) node [above left] {$\operatorname{Re} z$};
\draw [->] (0,-.5) -- (0,4) node [below right] {$\operatorname{Im} z$};
\end{scope}
\coordinate (o) at (0,0);
\coordinate (z1) at (4.511,1.642);
\coordinate (z2) at (2.143,2.553);
\coordinate (pr) at (1.368,3.759);
\coordinate (x) at (1,0);
\coordinate (y) at (0,1);
\draw (o) -- node[above,shift={(.4cm,.1cm)}] {$r_1$} (z1) node [right] {$z_1$};
\draw (o) -- node[above,yshift=.2cm] {$r_2$} (z2) node [right] {$z_2$};
\draw (o) -- node[above,yshift=1cm] {$r_1{\cdot}r_2$} (pr) node [right] {$z_1\cdot z_2$};
\draw pic[draw,red, "$\theta_1$", ->, angle eccentricity=1.2,angle radius = 1cm] {angle = x--o--z1};
\draw pic[draw,blue, "$\theta_2$", ->, angle eccentricity=1.2,angle radius = 1.5cm,pic text options={shift={(-3pt,3pt)}}] {angle = x--o--z2};
\draw pic[draw,violet, "$\theta_1{+}\theta_2$", ->, angle eccentricity=1.2,angle radius = 2.5cm] {angle = x--o--pr};
\end{tikzpicture}
\end{document}
In this case I think that we can add options to the angle label by putting them after the quotted text like that :
\draw pic[draw, "$\theta_2$"{option1,option2,...}, ->, angle eccentricity=1.2,angle radius = 1.5cm] {angle = x--o--z2};
the code
\documentclass{article}
\usepackage{tkz-euclide}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usetkzobj{all}
\usepackage{subcaption}
\usetkzobj{all}
\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}
\begin{tikzpicture}[scale=1]
\begin{scope}[thick,font=\scriptsize]
\draw [->] (-.5,0) -- (5.5,0) node [above left] {$\operatorname{Re} z$};
\draw [->] (0,-.5) -- (0,4) node [below right] {$\operatorname{Im} z$};
\end{scope}
\coordinate (o) at (0,0);
\coordinate (z1) at (4.511,1.642);
\coordinate (z2) at (2.143,2.553);
\coordinate (pr) at (1.368,3.759);
\coordinate (x) at (1,0);
\coordinate (y) at (0,1);
\draw (o) -- node[above,shift={(.4cm,.1cm)}] {$r_1$} (z1) node [right] {$z_1$};
\draw (o) -- node[above,yshift=.2cm] {$r_2$} (z2) node [right] {$z_2$};
\draw (o) -- node[above,yshift=1cm] {$r_1{\cdot}r_2$} (pr) node [right] {$z_1\cdot z_2$};
\draw pic[draw, "$\theta_1$", ->, angle eccentricity=1.2,angle radius = 1cm] {angle = x--o--z1};
\draw pic[ draw,->,blue, "$\theta_2$"{shift=(80:0.35),inner sep=1pt, circle,draw},angle eccentricity=1.1,angle radius = 1.5cm] {angle = x--o--z2};
\draw pic[draw, "$\theta_1{+}\theta_2$", ->, angle eccentricity=1.2,angle radius = 2.5cm] {angle = x--o--pr};
\end{tikzpicture}
\end{document}
Let us move labels by hand.
\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}[scale=2,thick]
\draw[->] (-.5,0)--(2.5,0) node[below]{\rm{Re}$z$};
\draw[->] (0,-.5)--(0,3) node[left]{\rm{Im}$z$};
\def\aone{20} \def\atwo{45}
\def\rone{2} \def\rtwo{1.6}
\draw
(0,0)--(\aone:\rone)
node[pos=.8,below]{$r_1$} node[right]{$z_1$}
(0,0)--(\atwo:\rtwo)
node[pos=.65,left]{$r_2$} node[above]{$z_2$}
(0,0)--(\aone+\atwo:\rone*\rtwo)
node[pos=.65,left]{$r_1\cdot r_2$} node[right]{$z_1\cdot z_2$};
\draw[->,red] (0:.5) arc(0:\aone:.5)
node[pos=.55,right]{$\theta_1$};
\draw[->,blue] (0:.8) arc(0:\atwo:.8)
node[pos=.75,right]{$\theta_2$};
\draw[->,magenta] (0:1.2) arc(0:\aone+\atwo:1.2)
node[pos=.55,right]{$\theta_1+\theta_2$};
\end{tikzpicture}
\end{document}