Has any equation with one unknown value a solution with complex numbers unless there's an indetermination or an impossible equality with numbers? An equation like the mentioned has no solution in cases like the following:
$x+2=x+3$ That would mean that if there was a solution then $ 2=3$, which is absurd.
Also an equation like $x/0=2$ has no solution, as it is an indetermination.
But maybe for the rest of the cases, this is possible, for example the function $1^x=2$ has no solution, in real numbers, but does in complex numbers. I'd like to know if this happens for every possible equation with one unknown value except for the cases I'm saying it would be impossible.
As indetermination, I mean the one when calculation a limit of a function that would be related to the equation.
For example $1/x=0$, would have no solution.
But, precisely, the limit of $1/x$ when $x$ tends to infinity would be $0$, which would be related to the equation

There is no real or complex solution to the equation $e^x=0$.
