First you should know the difference between these two term.
(1)Complement of Language
(2)Complement of Machine
Complement of Language
$L^{c}=\sum ^{*}-L$
Suppose you have language $L=a^{+}$ over $\sum =\left ( a \right )$.
$L^{c}=a^{*}-a^{+}$
So $L^{c}=\epsilon$
Complement of Machine
Let M be any finite automata then the complement of the machine can be obtained by swapping its accepting states with its non-accepting states and vice versa.Let us take an example,
This DFA accepts the language $L=\left \{ a,aa,aaa,aaaa,............ \right \}$
over the alphabet $\sum =\left ( a,b \right )$.
Now we will swap its accepting states with its non-accepting states and vice versa and will get the following −
This DFA accepts the language $L=\left \{ \epsilon ,b,ab,bb,....... \right \}$.
In case of DFA complementation the language is also complemented i.e.
$L(M^{c})=\left ( L\left ( M \right ) \right )^{c}$.
But this is not hold true in case of NFA , the language may or may not complemented.
That,s it.
