# How do I align equations with a column flush right?

I am using \documentclass{report}. I want to have the equation exactly as shown in the image attached.

This is what I got:

I have also tried

[ Q_k=\sum_{n=0}^{N-1} Q_{n}e^{-i(\frac{2\pi kn}{N})}]
k = 1,2,......,(N-1)

• How far have you gotten? What have you tried? Could you edit the relevant part of what you currently have into the question? – Davislor May 17 at 18:15
• Yes, I have tried. I have problem the part where k=1,2...,(N-1) – SANJAY S KUMAR May 17 at 18:16
• well provide a small complete document that (just) has the equation so far and say what error you got. don't make everyone offering to help type in the whole thing – David Carlisle May 17 at 18:18
• you could just use &k=0,... to get the side condition, – David Carlisle May 17 at 18:19
• You’re new here, but people normally post a Minimal (Non-)Working Example, so we can see what the specific problem is. – Davislor May 17 at 18:20

Another solution, with align* and the \mathrlap command from mathtools:

\documentclass{report}
\usepackage{mathtools}
\usepackage{showframe}
\renewcommand{\ShowFrameLinethickness}{0.2pt}

\newcommand\upi{\mathrm{i}} % The imaginary constant

\begin{document}

\begin{align*}
Q_k & = \sum_{n=0}^{N-1} Q_{n}e^{-\upi\bigl(\tfrac{2\pi kn}{N}\bigr)} \mathrlap{\hskip 4em k = 1,2,\dots,(N-1) }\\
e^{\upi Q} &= \cos Q + \upi \sin Q &
\end{align*}

\begin{align*}
Q_k & = \sum_{n=0}^{N-1} Q_{n}e^{-\upi\bigl(\tfrac{2\pi kn}{N}\bigr)} \\
e^{\upi Q} &= \cos Q + \upi \sin Q &
\end{align*}

\end{document}


If I understand what you want, perhaps this would work:

\documentclass{report}
\usepackage{amsmath}
\usepackage{lipsum}

\newcommand\upi{\mathrm{i}} % The imaginary constant

\begin{document}
\lipsum[1]

\begin{flalign*}
& & Q_k &= \sum_{n=0}^{N-1} Q_{n}e^{-\upi (\frac{2\pi kn}{N})} &  \qquad k = 1,2,......,(N-1) \\
& & e^{\upi Q} &= \cos Q + \upi \sin Q &
\end{flalign*}
\end{document}


This sets the system of equations into columns, spread out across the full width of the page. The first column is empty, the second and third align at the equals signs, and there is some extra space at the start of the last column. The starred environment suppresses an equation number.

Tweak the definition of \upi to how you want the imaginary constant i to appear. (Your sample seemed to use \mathrm{i}. I personally often use upright italics. Another common convention is \i.)

One way to write the equation set is

 \documentclass{report}
\usepackage{amsmath}

\begin{document}
\begin{align*}
Q_{k} &= \sum_{n=0}^{(N-1)} Q_{n} \, e^{-i \, \left(\frac{2 \pi k n}{N}\right)} \hspace{10mm} k = 0, 1, \cdots, N-10 \\
e^{i \, Q} &= \cos{Q} + i \, \sin{Q}
\end{align*}

\end{document}