@mommunism if he think infinity as a number instead of concept, then he is correct the fact that infinity times zero is indeed indeterminate form. However, I like to think infinity as a concept rather than number.
@jecko It definitely is a concept. The only reason that the result is undefined in that case is because it isn't a number, which makes the expression meaningless since you can't multiply non-numbers. We say that infinity multiplied by other numbers would still be infinity, but it would be a different infinity if infinity was actually a number (and that also proves it isn't one).
i don't understand about zero things, even a imaginary number multiplied by zero are zero (the phase where it as imaginary and real number at same time / they intersect at same point).