Centering the align environment on the middle column

Question

I have a set of aligned equations that I would like to provide an \implies for down the left hand side. I used this originally:

\begin{align}
    (x-1)^2 &= -1    \\
        x-1 &= \pm i \\
          x &= 1 \pm i
\end{align}

which results in a centred set of equations. Then added the \implies in a left column:

\begin{align}
    &          & (x-1)^2 &= -1    \\
    & \implies &     x-1 &= \pm i \\
    & \implies &       x &= 1 \pm i
\end{align}

However now the entire environment is shifted to the right. Is there a way to keep the original alignment?

Answer 1

If you want exactly the same alignment as before, but this time with \implies, this does the trick:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
  (x-1)^2 &= -1     \\
      x-1 &= \pm i  \\
        x &= 1 \pm i
\end{align}

\begin{alignat}{3}
           && (x-1)^2 &= -1      && \phantom{\implies} \\
  \implies &&     x-1 &= \pm i   && \\
  \implies &&       x &= 1 \pm i &&
\end{alignat}
\end{document}

The idea here is to duplicate the width of \implies on the left with a \phantom{\implies} on the right, thereby evenly spacing the equation/environment again.

Answer 2

Removing the first alignment character and adding a few \phantoms should do the trick. Alternatively you can use alignat:

\begin{document}
\begin{align}
    (x-1)^2 &= -1    \\
        x-1 &= \pm i \\
          x &= 1 \pm i
\end{align}

\begin{align}
    \phantom{\implies}    (x-1)^2 &= -1    \\
    \implies\phantom{()^2}    x-1 &= \pm i \\
    \implies\phantom{({}-1)^2}  x &= 1 \pm i
\end{align}

 \begin{alignat}{3}
             && (x-1)^2 &= -1    \\
    \implies &&     x-1 &= \pm i \\
    \implies &&       x &= 1 \pm i
 \end{alignat}
 \end{document}