%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
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\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
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\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
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% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

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% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
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%■等号付き不等号 by 美文書作成入門
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% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

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\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■


\begin{frame}[t]
\frametitle{複素数の除法（有理化もどき）}
%\vskip-2ex
\setbeamercolor{CUDCream50}{fg=black,bg=CUDCream!50}
\centerline{%
\begin{minipage}[c]{0.76\textwidth}
\large
\begin{beamercolorbox}[wd=\textwidth,ht=2.2ex,dp=1ex,shadow=true,
	rounded=true, center]{CUDCream50}
\( (\text{○}\textcolor{CUDRed}{\text{＋}}\text{□})
	(\text{○}\textcolor{CUDBlue}{\text{－}}\text{□})
	=\text{○}^2\text{－}\text{□}^2 \)
\end{beamercolorbox}
\end{minipage}
}

\vskip3ex
\setbeamercolor{CUDBrightCyan50}{fg=black,bg=CUDBrightCyan!50}
\centerline{%
\begin{minipage}[c]{0.76\textwidth}
\large
\begin{beamercolorbox}[wd=\textwidth,ht=2.2ex,dp=1ex,shadow=true,
	rounded=true, center]{CUDBrightCyan50}
\( (\text{○}\textcolor{CUDBlue}{\text{－}}\text{□})
	(\text{○}\textcolor{CUDRed}{\text{＋}}\text{□})
	=\text{○}^2\text{－}\text{□}^2 \)
\end{beamercolorbox}
\end{minipage}
}

\bigskip
\centerline{を使う}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{複素数の除法（有理化もどき）}
\vskip-2zh
\begin{eqnarray*}
	\myfrac{\text{△}}{\text{○}\textcolor{CUDRed}{\text{＋}}\text{□}\, i} %
		&=& \pause \myfrac{\text{△}\textcolor{CUDCyan}{(\text{○}\textcolor{CUDBlue}{\text{－}}\text{□}\, i)} }{ %
	(\text{○}\textcolor{CUDRed}{\text{＋}}\text{□}\, i)\textcolor{CUDCyan}{(\text{○}\textcolor{CUDBlue}{\text{－}}\text{□}\, i)}}
\end{eqnarray*}

\vskip2zh
\Large
\centerline{\textcolor{CUDRed}{＋}のときは\textcolor{CUDBlue}{－}をかけ算する}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{複素数の除法（有理化もどき）}
\vskip-2zh
\begin{eqnarray*}
	\myfrac{\text{△}}{\text{○}\textcolor{CUDBlue}{\text{－}}\text{□}\, i} %
	&=& \pause \myfrac{\text{△}\textcolor{CUDCyan}{(\text{○}\textcolor{CUDRed}{\text{＋}}\text{□}\, i)} }{ %
	(\text{○}\textcolor{CUDBlue}{\text{－}}\text{□}\, i)\textcolor{CUDCyan}{(\text{○}\textcolor{CUDRed}{\text{＋}}\text{□}\, i)}}
\end{eqnarray*}

\vskip2zh
\Large
\centerline{\textcolor{CUDBlue}{－}のときは\textcolor{CUDRed}{＋}をかけ算する}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\text{○}+\text{△}i$の形へ（その$1$）}
\vspace*{-4ex}
\begin{eqnarray*}
\myfrac{3 }{ 4 \alt<2->{\textcolor{CUDRed}{{}+{}}}{+} i} \pause\pause &=& 
	\myfrac{3\,\textcolor{CUDBlue}{(4-i)} }{ (4 \textcolor{CUDRed}{{}+{}} i)\textcolor{CUDBlue}{(4-i)}}\pause\\[1ex]
	&=& \myfrac{12-3i }{ \hooklen{(4+i)(4-i)}{4^2- 
		\alt<5->{\textcolor{CUDGreen}{i^2}}{i^2}}} \hskip1zw\pause
	\textcolor{CUDGreen}{\text{【\ }i^2=-1\ \text{】}}\pause\\[1ex]
	&=& \myfrac{12-3i }{ \hooklen{(4+i)(4-i)}{16-\textcolor{CUDGreen}{(-1)}}}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\text{○}+\text{△}i$の形へ（その$1$）}
\vspace*{-4ex}
\begin{eqnarray*}
	&=& \myfrac{12-3i }{ \hooklen{(4+i)(4-i)}{16-(-1)}} \\[1ex]
	&=& \myfrac{12-3i }{ \hooklen{(4+i)(4-i)}{17}} \\[1ex]
	&=& \myfrac{\,12\,}{17}-\myfrac{3 }{\,17\,}\ i
		\quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\text{○}+\text{△}i$の形へ（その$2$）}
\vspace*{-4ex}
\begin{eqnarray*}
\myfrac{1+i }{ 3 \alt<2->{\textcolor{CUDBlue}{{}-{}}}{-} 2i} \pause\pause &=& 
	\myfrac{(1+i)\textcolor{CUDRed}{(3+2i)} }{ (3 \textcolor{CUDBlue}{{}-{}} 2i)\textcolor{CUDRed}{(3+2i)}}\pause\\[1ex]
	&=& \myfrac{3+2i+3i+2i^2 }{ 3^2- (2i)^2}
		\hskip1zw\pause\\[1ex]
	&=& \myfrac{3+\hooklen{2i+3i}{5i}+2\alt<6->{\textcolor{CUDGreen}{i^2}}{i^2} }{
			9- 4
		\alt<6->{\textcolor{CUDGreen}{i^2}}{i^2}} \hskip1zw\pause
	\textcolor{CUDGreen}{\text{【\ }i^2=-1\ \text{】}}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\text{○}+\text{△}i$の形へ（その$2$）}
\vspace*{-4ex}
\begin{eqnarray*}
	&=& \myfrac{3+5i+2\textcolor{CUDGreen}{i^2} }{
			9- 4 \textcolor{CUDGreen}{i^2}} \hskip3zw
	\textcolor{CUDGreen}{\text{【\ }i^2=-1\ \text{】}}\\[1ex]
	&=& \myfrac{3+5i+2\!\times\!\textcolor{CUDGreen}{(-1)} }{
			9- 4 \!\times\!\textcolor{CUDGreen}{(-1)}}\\[1ex]
	&=& \myfrac{3+5i\hooklen{+2\!\times\!(-1)}{-2} }{9+4}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{$\text{○}+\text{△}i$の形へ（その$2$）}
\vspace*{-4ex}
\begin{eqnarray*}
	&=& \myfrac{3+5i-2 }{ 9+ 4}\\[1ex]
	&=& \myfrac{\hooklen{3+5i-2}{1+5i} }{ 13}\\[1ex]
	&=& \myfrac{1}{\,13\,}+\myfrac{5 }{\,13\,}\ i
		\quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}

\textcolor{CUDRed}{

