in my algebra book,there is written following well known identity
$e^{2*\pi*i}=1$
generally we can use also this identity $e^{k*\pi*i}=(-1)^k$
and if instead of $k$,we put $2$ we get $(-1)^2=1$
but know book asks what is wrong with following thing: $e^{2*a*\pi*i}=e^{(2*\pi*i)*a}=1^a=1$?
i have tried to figure out if what kind of $a$ gives me wrong result,i was thinking that $a=1/2$,as it would be $\sqrt{1}=1$ and $\sqrt{1}=-1$ and second case makes this wrong,but i am not sure if this is correct way.if $a=0$ then everything is ok,but if $a<0$ then it makes i think wrong,because $1^k$ for all $k$ is $1$,but on the other hand because
$e^{k*\pi*i}=(-1)^k$ and $k=2*a$ it maybe square root from negative number,which is complex number and not equal to $1$,am i wrong?please help me