2
    \begin{Question}{1}
    Part 1) prove $f+g$ is holomorphic at $z_0$.\\
    \\
    We want to show that $(f+g)'(z_0)$ exists:\\
    \\
    $$ (f+g)'(z_0) =\lim_{z \to z_0} \frac{(f+g)(z) - (f+g)(z_0)}{z-z_0}$$\\
    $$ =\lim_{z \to z_0} \frac{f(z)+g(z)- f(z_0)-g(z_0)}{z-z_0}$$\\
    $$=\lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0} + \lim_{z \to z_0} 
    \frac{g(z)-g(z_0)}{z-z_0}$$\\
    $$ = f'(z_0) + g'(z_0)$$


    \end{Question}

I tried to use \begin{aligned} \end{aligned} but it comes one line

Now My test looks like this enter image description here

How can I flushleft them? I don't want horizontal alignment!

2
  • 3
    you should not use $$ in latex (and certainly never follow it by \\ if you use latex markup then using [fleqn] option on \documentclass would cause all equations to be left aligned. Sep 6, 2017 at 22:05
  • 1
    See the documentation of amsmath and its align environment, for example
    – user31729
    Sep 6, 2017 at 22:05

3 Answers 3

4

Here are two solutions that use an aligned environment. In the first, all four rows of the multi-line equation are left-aligned, as you seem to desire. In the second, alignment is on the = symbols. The only difference between the code chunks is in the placement of the & alignment specifier in row 1.

(Speaking for myself, I prefer the second solution.)

enter image description here

\documentclass{article} 
\usepackage{amsmath}

\begin{document}
Prove $f+g$ is holomorphic at $z_0$.

We want to show that $(f+g)'(z_0)$ exists:

\smallskip\noindent
$\begin{aligned}
&(f+g)'(z_0) =\lim_{z \to z_0} \frac{(f+g)(z) - (f+g)(z_0)}{z-z_0}\\
&=\lim_{z \to z_0} \frac{f(z)+g(z)- f(z_0)-g(z_0)}{z-z_0}\\
&=\lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0} + \lim_{z \to z_0} 
    \frac{g(z)-g(z_0)}{z-z_0}\\
&= f'(z_0) + g'(z_0)
\end{aligned}$

\bigskip\noindent
$\begin{aligned}
(f+g)'(z_0) &=\lim_{z \to z_0} \frac{(f+g)(z) - (f+g)(z_0)}{z-z_0}\\
&=\lim_{z \to z_0} \frac{f(z)+g(z)- f(z_0)-g(z_0)}{z-z_0}\\
&=\lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0} + \lim_{z \to z_0} 
    \frac{g(z)-g(z_0)}{z-z_0}\\
&= f'(z_0) + g'(z_0)
\end{aligned}$
\end{document}
4

i suppose, that you looking for something like this:

enter image description here

\documentclass{article}
\usepackage{amsmath}

\begin{document}
Part 1) prove $f+g$ is holomorphic at $z_0$.

\bigskip
We want to show that $(f+g)'(z_0)$ exists:
    \begin{align*}
(f+g)'(z_0) 
    & = \lim_{z \to z_0} \frac{(f+g)(z) - (f+g)(z_0)}{z-z_0}    \\
    & = \lim_{z \to z_0} \frac{f(z)+g(z)- f(z_0)-g(z_0)}{z-z_0} \\
    & = \lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0} 
                + \lim_{z \to z_0} \frac{g(z)-g(z_0)}{z-z_0}    \\
    &  = f'(z_0) + g'(z_0)
    \end{align*}
\end{document}
2
  • That is good, but can I make the last two lines tidier, cause that looks a bit ugly... Thank you so much!
    – user142872
    Sep 6, 2017 at 22:24
  • @user142872, well i didn't care much about math meaning of your equation, but focused only on latex aspect (to which is this site dedicated). now is corrected also the math aspect of your equation (what should not be so difficult to do by you after showing principle, how to use amsmath math environments). happy tex-ing!
    – Zarko
    Sep 6, 2017 at 23:41
2

You have the fleqn environment, defined by nccmath, which works somewhat like subequations : all displayed equations inside this environment will be flushleft. It accepts an optional argument – the distance from the left margin at which the environment begins (0 by default). Here I chose \parindent:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{amsmath, nccmath}

\begin{document}
Part 1) prove $f+g$ is holomorphic at $z_0$.

\bigskip
We want to show that $(f+g)'(z_0)$ exists:
\begin{fleqn}[\parindent]
\begin{align*}
(f+g)'(z_0)
    & = \lim_{z \to z_0} \frac{(f+g)(z) - (f+g)(z_0)}{z-z_0} \\
    & = \lim_{z \to z_0} \frac{f(z)+g(z)- f(z_0)-g(z_0)}{z-z_0} \\
    & = \lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0} + \lim_{z \to z_0} \frac{g(z)-g(z_0)}{z-z_0}\\
    & = f'(z_0) + g'(z_0)
    \end{align*}
\end{fleqn}

\end{document} 

enter image description here

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