Is there any other constant which satisfy Euler formula? Every body knows Euler Formula

$e^{ix}=\cos x +i\sin x$

Is there any other constant beside $i$ which satisfies the above equation?
 A: If you write $\cos(x) = \frac{e^{ix} + e^{-ix}}{2}, \sin(x) = \frac{e^{ix}-e^{-ix}}{2i}$, then any constant $k$ for which this is true has $e^{kx}$ as a linear combination of $e^{ix}, e^{-ix}$.  From linear independence of the functions $e^{kx}$ for $k\in \mathbb{C}$, we can conclude that $k = \pm i$.
A: If I understand correctly  your question  you ask about the
                  equation exp(ax) = cos(x) + asin(x) ; a ≠ i, not for equality of functions but for 
                  equality of numbers. We see the problem from the two viewpoints.
                       For real functions it is clear that it is impossible. On the 
complex we would have the equality exp(ax) – exp(ix) = (a -i)sin(x); taking the 
second derivative and adding we get (a^2  + 1) exp(ax) = 0 so still impossible. 
                      For diophantine equations there are for each negative 
constant a, an infinity of positive x with couples (x,a) satisfying the equality
 which is clear because of intersections of both curves.
