\documentclass[twocolumn]{article}
\pagestyle{empty}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multicol}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
\oddsidemargin=0pt
\topmargin=0pt
\textwidth=6.5in
\textheight=8.5in
\begin{document}
\textcolor{cyan}{\Large \bfseries{8.1 Complex Numbers}}
\begin{multicols}{2}
\begin{minipage}[t]{0.2\textwidth}
\begin{itemize}
\item Basic Concepts of Complex Numbers
\item Complex Sloutions of Equations
\item Operations on Complex Numbers
\end{itemize}
{\bfseries \textcolor {brown}{LOOKING AHEAD TO CALCULUS}}\\
The letters \textit {j} and \textit {k} are also used to rep-
resent $\sqrt -1$ in calculus and some
applications (electronics, for example)\\
\\
The cslculator is in complex number
mode. The top screen supports the
definition of i. The bottom screen shows how the calculator returns the
real and imaginary parts of the
complex number $7 + 2i$
\end{minipage}
\begin{minipage}[t]{0.8\textwidth}
{\bfseries \textcolor{cyan}{Basic Concepts of Complex Numbers}} The set of real numbers does not include
all numbers needed in algebra. For example, there is no real number solution of
the equation
\begin{center}
{$x^2=-1,$}
\end{center}
since no real number , when squared, gives -1. To extend the real number system
to include solutions of equations of this type, the number $i$ is defined to
have the following property.
\\
\\
{\bfseries \textcolor{brown}{The Imaginary Unit $i$}}
\\
\begin{center}
$i=\sqrt-1$ and therefore $i^2=-1$.
\end{center}
(Note that $-i$ is also a square root of -1.)
\\
\\
Square roots of negative numbers were not incorporated into an integrated
number system until the 16th century. They were then used as solutions of equa-
tions and later (in the 18th century) in surveying. Today, such numbers are used
extensively in science and engineering.
{\textit Complex numbers} are formed by adding real numbers and multiples of $i$.
\\
\\
{\bfseries \textcolor {brown}{Complex Numbers}}
\\
If a and b are real numbers, then any number of the form $a + bi$ is a
{\bfseries complex number.} in the complex number a+bi,a is the {\bfseries real part} and b is the {\bfseries imaginary part.}*
\\
Two complex numbers a+bi and c+di are equal provided that their real
parts are equal and that their imaginary parts are equal; that is, they are equal if and
only if a=c and b=d. Some graphing calculators, such as the TI-83/84 Plus, are capable of
working with complex numbers, as seen in {\bfseries Figure1.} For a complex number $a+bi,$ if $b=0,$ then $a+bi=a,$ which is a real
number. Thus, the set of real numbers is a subset of the set of complex numbers.
If $a=0$ and $b 0$, the complex number is said to be a {\bfseries pure imaginary number.}
For example, $3i$ is a pure imaginary number. A pure imaginary number, or a
number such as $7+2i$ with $a 0$ and $b 0$, is a {\bfseries nonreal complex number.}
(The from a+ib is used to write expressions such as $i\sqrt 5$, since $\sqrt 5i$ could
be mistaken for $\sqrt 5i$.)
The relationships among the subsets of the complex numbers are shown in
{\bfseries Figure 2} of the next page.
\end{minipage}
\end{multicols}
\newpage
For a positive real number \textit {a}, the expression $\sqrt -a$ is defined as follows.
---Britney Wiggins
\end{document}`
答案1
也许您需要说一下该文档的目的，然后我们可以建议一些标记。
\documentclasss[twocolumn]{article}
因此该文档有 2 列（使用标准的 2 列实现）
\pagestyle{empty}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multicol}
multicol 不兼容[twocolumn]，您会收到警告
Package multicol Warning: May not work with the twocolumn option on input line
\oddsidemargin=0pt
\topmargin=0pt
\textwidth=6.5in
\textheight=8.5in
\begin{document}
\textcolor{cyan}{\Large \bfseries{8.1 Complex Numbers}}
这样文本就会进入标准乳胶第一列。
\begin{multicols}{2}
然后尝试在第一列中启动一个平衡的 2 列区域，如前所述，这通常不起作用（如果它起作用，您将有 4 列）
\begin{minipage}[t]{0.2\textwidth}
这样就会形成一个占总宽度 0.2（而不是当前列的宽度）的框，这意味着里面的文本不能换到另一列。
\begin{minipage}[t]{0.8\textwidth}
这样就使得盒子的宽度占总宽度的 0.8，无论有 2 列还是 4 列，都不可能容纳在一列中。
因此，首先您需要说明是否要使用标准 latex[twocolumn]或multicol软件包。每种方法都有优点和缺点，但如果同时使用这两种方法，则会同时获得两者的缺点，而没有任何优点。
其他的建议。
不要使用\\强制分段，请使用空行。不要“手动”为每个标题着色，只需使用章节标记并在序言中定义章节格式。不要使用\textit来表示数学变量，使用\(或$。不要使用\begin{center}$...来居中显示数学，也不要手动编号，始终让 latex 处理数字，使用\ref和\label。
因此，我会从类似这样的、运行时没有警告或错误的东西开始，然后根据需要添加样式。
\documentclass{article}
\pagestyle{empty}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multicol}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
\begin{document}
\setcounter{section}{8}
\subsection{Complex Numbers}
\begin{itemize}
\item Basic Concepts of Complex Numbers
\item Complex Sloutions of Equations
\item Operations on Complex Numbers
\end{itemize}
\subsubsection{LOOKING AHEAD TO CALCULUS}
The letters $j$ and $k$ are also used to represent $\sqrt -1$ in calculus and some
applications (electronics, for example)
The calculator is in complex number
mode. The top screen supports the
definition of $i$. The bottom screen shows how the calculator returns the
real and imaginary parts of the
complex number $7 + 2i$
\subsection{Basic Concepts of Complex Numbers}
The set of real numbers does not include
all numbers needed in algebra. For example, there is no real number solution of
the equation
\[
x^2=-1,
\]
since no real number , when squared, gives -1. To extend the real number system
to include solutions of equations of this type, the number $i$ is defined to
have the following property.
\subsection{The Imaginary Unit $i$}
\begin{center}
$i=\sqrt-1$ and therefore $i^2=-1$.
\end{center}
(Note that $-i$ is also a square root of -1.)
Square roots of negative numbers were not incorporated into an integrated
number system until the 16th century. They were then used as solutions of equa-
tions and later (in the 18th century) in surveying. Today, such numbers are used
extensively in science and engineering.
\textit{Complex numbers} are formed by adding real numbers and multiples of $i$.
\subsection{Complex Numbers}
If a and b are real numbers, then any number of the form $a + bi$ is a
{\bfseries complex number.} in the complex number a+bi,a is the {\bfseries real part} and b is the {\bfseries imaginary part.}*
Two complex numbers a+bi and c+di are equal provided that their real
parts are equal and that their imaginary parts are equal; that is, they are equal if and
only if $a=c$ and $b=d$.
Some graphing calculators, such as the TI-83/84 Plus, are capable of
working with complex numbers, as seen in \ref{fig}
For a complex number $a+bi,$ if $b=0,$ then $a+bi=a,$ which is a real
number. Thus, the set of real numbers is a subset of the set of complex numbers.
If $a=0$ and $b 0$, the complex number is said to be a {\bfseries pure imaginary number.}
For example, $3i$ is a pure imaginary number. A pure imaginary number, or a
number such as $7+2i$ with $a 0$ and $b 0$, is a {\bfseries nonreal complex number.}
(The form $a+ib$ is used to write expressions such as $i\sqrt 5$, since $\sqrt 5i$ could
be mistaken for $\sqrt 5i$.)
The relationships among the subsets of the complex numbers are shown in
\ref{figg} of the next page.
\newpage
For a positive real number $a$, the expression $\sqrt -a$ is defined as follows.
---Britney Wiggins
\begin{figure}
xxx\caption{x}\label{fig}
\end{figure}
\begin{figure}
yyy\caption{y}\label{figg}
\end{figure}
\end{document}
答案2
我不知道你到底想实现什么，但是：
我删除了全局twocolumn选项并进行编译，得到了这个
这是你想要的吗？
或者，如果我保留该twocolumn选项，并删除minipages 和multicolumns，我会得到
如果您不想要这些，您应该提供更详细的信息！
使用书籍类
book将类与包一起使用marginnote似乎可以提供您想要的行为。
\documentclass[twoside,a4letter]{book}
\usepackage{marginnote}
\usepackage{lipsum}
\begin{document}
\lipsum[1-2]
\marginnote{This is a margin note}
\lipsum[3-4]
\end{document}
产量
