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I wanted to write down an equation however it seems that whenever I use \pi I keep on getting Missing $ inserted error Here is my code:

$u_k = 2\cos(2^kr\pi)$
\subsection{Create an equation for $u\textsubscript{k+1}$  using $u_k$}
$u_k = 2 \times  \Re(e\textsuperscript{2ir$\pi$ })$ 
\\
$u\textsubscript{k+1}
=  2 \times \Re(e\textsuperscript{2\textsuperscript{k+1}ir\pi })
= 2 \times \Re(e\textsuperscript{2\superscript{k}ir\pi }\textsuperscript{2})
\Leftrightarrow
\\ 
2 \times( \cos^2(2^kr\pi ) - \sin^2(2^kr\pi ) )= 4\cos^2(2^kr\pi ) - 2$

Here of a few of my many errors:

! Missing $ inserted.
<inserted text> 
                $
l.125 ...superscript{2\textsuperscript{k+1}ir\pi }
                                                  )
? 
! Extra }, or forgotten $.
\mbox  #1->\leavevmode \hbox {#1}
                                 
l.125 ...superscript{2\textsuperscript{k+1}ir\pi }
                                                  )
? 

Just in case it matters I'm using the amsmath package.

Thanks

5
  • 2
    Welcome. For superscripts in math mode there is ^: e^{2^{k+1}ir\pi} is the correct code. Similarly $u_{k+1}$ for subscripts. – egreg Aug 17 '20 at 16:54
  • Hmm, It doesn't seem to work. The errors are excactly the same. – scaraven Aug 17 '20 at 17:05
  • 1
    Fix \Re(e\textsuperscript{2ir$\pi$ }) into \Re(e^{2ir\pi}) – egreg Aug 17 '20 at 17:13
  • Thanks it works now. – scaraven Aug 17 '20 at 17:20
  • \textsuperscript is for when you're in text mode, and what's inside is also in text mode. – Teepeemm Aug 17 '20 at 17:44
2

I supposed it is something like this you're trying to obtain:

\documentclass{article}%
\usepackage{nccmath, mathtools}
\usepackage{amssymb} 
\begin{document}

$u_k = 2\cos(2^kr\pi)$
\subsection{Create an equation for \boldmath $u_{k+1}$ using $u_k$}
\begin{fleqn}
 \begin{alignat*}{2}
  u_k = {}& 2 \times \Re(e^{2ir\pi}) & & \\
u_{k+1}={} & 2 \times \Re(e^{2^{k+1}ir\pi }) = 2 \times \Re(e^{2^{k}ir\pi^{2}}) & & \\[-1ex]
\ArrowBetweenLines*[\Updownarrow]
 & 2 \times( \cos^2(2^kr\pi ) - \sin^2(2^kr\pi ) )= 4\cos^2(2^kr\pi ) - 2
\end{alignat*}
\end{fleqn}

\end{document} 

enter image description here

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