\documentclass{jarticle}

%				パッケージ読込
\usepackage{pstricks}%		PSTricksパッケージ
\usepackage{pst-eps}%
\usepackage{pst-plot}%
\usepackage{pst-node}%

\begin{document}

\TeXtoEPS   % Make an EPS picture out of .dvi file, with dvips -E.
% PSTricks Picture環境 and 設定
\psset{unit=10mm}\pspicture(-4.1,-2.1)(4.2,4.75)

% グリッド(編集中に使用)
%\psgrid[subgriddiv=1,griddots=5,gridlabels=5pt](-5,-3)(6,6)

	\psaxes[linecolor=black,linewidth=1.2pt,labels=none,ticks=none]{-}(0,0)(-3,-2)(3,4.2)

	\pcarc[linewidth=.9pt,arcsepA=2pt]{-}(1.145,2.2)(.53,2.38)
	\pcarc[linewidth=.9pt,arcsepA=2pt]{-}(-1.19,.475)(-1,0)
	\psarcn[linewidth=.9pt,arcsepA=2pt]{-}(1.6,0){.5}{105}{0}

	\pscustom[linewidth=1pt,linecolor=blue]{
	\psline{-}(-1.6,0)(1,2.9)(1.6,0)
	}

	\pscustom[linewidth=1pt,linecolor=red]{
	  \pscircle(0,1.2){2}
	}

	\psdots(1,2.9)

	\pcarc[linecolor=gray,linewidth=.9pt,arcsepA=2pt]{<-}(.85,2.5)(2,2.85)
	\pcarc[linecolor=gray,linewidth=.9pt,arcsepA=2pt]{<-}(-1.25,.2)(-2,-.9)

% テキスト
	\rput[l]{0}(1.2,3){\Large$z$}
	\rput[l]{0}(-.4,-.3){{\large$O$}}
	\rput[l]{0}(3.2,0){{\large$x$}}
	\rput[c]{0}(0,4.4){{\large$y$}}
	\rput[l]{0}(1.7,-.25){{\large$1$}}
	\rput[r]{0}(-1.7,-.25){{\large$-1$}}
	\rput[c]{46}(-.8,1.4){{\large$z+2$}}
	\rput[l]{0}(2.2,.5){{\large$\mathrm{arg}\,(z-1)$}}
	\rput[l]{-78}(1.45,1.9){{\large$z-2$}}
	\rput[r]{0}(-2.1,-.9){{\large$\mathrm{arg}\,(z+1)$}}
	\rput[l]{0}(2.1,2.9){{$\displaystyle\mathrm{arg}\,\left(\frac{\,z-1\,}{z+1}\right)
				\,=\, \frac{\pi}{4}$}}

\endpspicture
\endTeXtoEPS

\end{document}