Horizontal alignment of two lines of text

Question

I am trying to horizontally align the words "if", as depicted in the image below.

I have tried to use a minipage environment, but this did not yield the desired result. The code for this section of text is shown below.

\documentclass[a4paper,12pt]{extarticle}

\usepackage{graphicx,float}
\usepackage{amsmath}
\usepackage{amsfonts} 
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{float}

\begin{document}
\textit{Case 2}: 
If $s=0$, then 
\[\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} 1=N.\] If $s=N$, then 
\[\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} \exp (2\pi ir)=\sum_{r=1}^{N} [\cos(2\pi r)+i\sin(2\pi r)]=N.\]
\end{document}

Answer 1

A simple solution in this case is to use an \hphantom{}:

\hphantom{\textit{Case 2}:}

There are two outcomes, depending on if the initial indent was desired or not:

Notes:

• Besides \hphantom{} which provides the exact horizontal space as its paramter, there is als \vphantom{} which provides only the vertical spacing (with zero horizontal space). For this case you could also have just used the \phatom{} macro which inserts both the horizontal and vertical spacing of its parameter.

Code:

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\noindent
\textit{Case 2}: 
If $s=0$, then 
\[\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} 1=N.\] 
\hphantom{\textit{Case 2}:}
If $s=N$, then 
\[\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} \exp (2\pi ir)=\sum_{r=1}^{N} [\cos(2\pi r)+i\sin(2\pi r)]=N.\]

\hrule\medskip\par

\textit{Case 2}: 
If $s=0$, then 
\[\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} 1=N.\] 

\hphantom{\textit{Case 2}:}
If $s=N$, then 
\[\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} \exp (2\pi ir)=\sum_{r=1}^{N} [\cos(2\pi r)+i\sin(2\pi r)]=N.\]
\end{document}

Answer 2

Do you mean like this?:

\documentclass[a4paper,12pt]{extarticle}

\usepackage{graphicx,float}
\usepackage{amsmath}
\usepackage{amsfonts} 
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{float}

\begin{document}
        
\begin{align*}  
\textit{Case 2}:\quad
&\text{If} s=0, \text{then}
\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} 1=N. \\
&\text{If} s=N, \text{then}
\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} \exp (2\pi ir)=\sum_{r=1}^{N} [\cos(2\pi r)+i\sin(2\pi r)]=N.
\end{align*}

\end{document}

or

\documentclass[a4paper,12pt]{extarticle}

\usepackage{graphicx,float}
\usepackage{amsmath}
\usepackage{amsfonts} 
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{float}

\begin{document}
        
\begin{align*}  
\textit{Case 2}:\quad
&\text{If}\quad s=0, \text{then}\\
&\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} 1=N. \\
&\text{If}\quad s=N, \text{then}\\
&\sum_{r=1}^{N} \exp\left(\frac{2\pi irs}{N}\right)=\sum_{r=1}^{N} \exp (2\pi ir)=\sum_{r=1}^{N} [\cos(2\pi r)+i\sin(2\pi r)]=N.
\end{align*}

\end{document}