Undefined points of a function

1. Square1

123
Apart from visualizing firstly the maximum bounds of a function on a graph (domain), what are algebraic indications that some complex function does not exist at a given point? I know that if you evaluate a function that results in dividing by zero, the point is undefined. If you end up taking a square root of a negative number, the point was undefined.

Are there other ways to conclude the point does not exist on the function? Is there a formula that spits out the points that are undefined of a function?

2. skiller

237
Do you mean complex as in complicated or as in real+imaginary?
Evidently not the latter.