Sure, they do have applications in real life, but I am a person that goes with absolute logic, so I can't even understand how they can call those numbers "imaginary", but at the same time saying that they are real?! It doesn't make sense at all!
If you really were a person that goes with absolute logic, Math would be your favorite subject. Because math is only logic. It's deducing conclusions from hypotheses... without caring about the fact those hypotheses might never get true in real life and without caring about a possible application for the conclusion because that's physicists' job. All we care about is the logic that led from the hypotheses to the conclusion.
And no one said that those "imaginary" numbers were "real". On the contrary, most of the time they are not (they are in C, not bounded to R). C is actually a plane where R is a line (included in C), which allows you to solve more probems, including ones from R. Just imagine that R only allows you to walk on the ground and C allows you to fly (ok, in my example I'm doing 2D→3D but it's still adding a dimension, like 1D→2D).
And you should not complain too much about complexes because if you take higher level maths, you'll deal with spaces that don't even contain numbers, with dimensions that can be more than 4, even infinite, so if you can't picture numbers on a 2D plane, you won't get anything that you're told there
It's incredibly tiring and boring, but if you get distracted even for a moment, you will be left behind so easily! It's annoying, I missed just ONE class because I overslept and didn't go and I missed out on so many things, that I couldn't even catch up! We are talking about missing ONE 2-hour-long session and being left behind so much, you lose all hope!
Lol, I don't agree about the distraction part
When I was in high school, I was in the last row in the classroom, programming things on my calculator without listening to the teacher (because last time I listened, he said something he already said before) and still had the best grades in my class (not true for other subjects though
). And even at the final high school exam (baccalauréat), I spent more time playing Chess on my calculator than thinking about the exam, and only answered questions because I was losing at Chess (not the game I'm best at
)... and I still got my best grade for the exam in Maths (I don't remember what, but I know it was above 18/20 or I would have been disappointed, which I was not).