2
\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}`
2
  • Why are you using multicolumn on your document, if already have turned ON the twocolumns global option? Use one of them... I guess the compiler is confused
    – Dox
    Oct 4, 2013 at 13:47
  • Welcome to TeX.SX! Please add a minimal working example (MWE) that illustrates your problem. It will be much easier for us to reproduce your situation and find out what the issue is when we see compilable code, starting with \documentclass{...} and ending with \end{document}. Oct 4, 2013 at 21:56

2 Answers 2

6

perhaps you need to say what this document is trying to do, then we could suggest some markup.

\documentclasss[twocolumn]{article}

So the document is 2 column (using the standard 2-column implementation)

\pagestyle{empty}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multicol}

multicol is incompatible with [twocolumn] and you get a warning

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}}

so that text is going in to the standard latex first column.

\begin{multicols}{2}

This then tries to start a balanced 2 column region within the first column, which as noted typically does not work (if it did work you would have 4 columns)

\begin{minipage}[t]{0.2\textwidth}

This then makes a box .2 of the total width (rather than the width of the current column) which means the text inside can not break to another column.

 \begin{minipage}[t]{0.8\textwidth}

And this makes a box .8 of the total width which can not possibly fit in a column whether you have 2 or 4 columns.

So first you need to state whether you want to use the standard latex [twocolumn] or the multicol package. Each has advantages and disadvantages, but if you use both you get the disadvantages of both and no advantages at all.

Other comments.

Don't use \\ to force paragraph breaks, use a blank line. Don't colour each heading "by hand" just use section markup and define the section formatting in the preamble. don't use \textit for math variables,, use \( or $. Don't use \begin{center}$... to centre display math, and don't number things by hand always let latex hande the numbers ad use \ref and \label.

So I'd start from something like this which runs without warning or error, then add styling as required.

\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}
3

I don't know exactly what you want to achieve, but:

I delete the global twocolumn option and compile and got this

enter image description here

Was it what you want?

Alternatively, If I leave the twocolumn option, and delete the minipages and multicolumns, I get

enter image description here


If you wanted none of this, you should include more detailed information!



Using the book class

Using the book class together with marginnote package seems to provide the behaviour you wanted.

\documentclass[twoside,a4letter]{book}
\usepackage{marginnote}
\usepackage{lipsum}

\begin{document}
\lipsum[1-2]
\marginnote{This is a margin note}
\lipsum[3-4]
\end{document}

yields

enter image description here

2
  • We have to mimic a math book, which is why I was trying to do the two columns. If I take out [twocolumn] what to I need to add/subtract because when I did remove it I got an error @dox Oct 7, 2013 at 14:51
  • @BritneyWiggins Could you post a picture (or sketch) of what you want to achieve? BTW, in the book class there is a way to write on the margins (if that is your purpose)
    – Dox
    Oct 7, 2013 at 18:25

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