Is this correct and enough proof

$\displaystyle (cosx+isinx)^n=cos(nx)+isinx$ is true so i put 1 and its true now ima prove for

$\displaystyle S(k+1) = (Cosx+isinx)^k+1= (Cosx+isinx)^k(cosx+isinx)$ now we can rewrite that ^k with a formula i cant remember as

$\displaystyle (coskx+isinkx)(cosx+isinx)$

and now i foctour out cos x and sin x

$\displaystyle Cos x ( k+1) + iSinx(k+1)$

is this enough