I managed to get complex numbers into a 4u exam by using completely the wrong, strangest method on earth, the real question is how I managed to get the correct answer! (through doing it correctly, I know I did). I realize now what I did.
The question was something like this:
If the cost of making a certain trip in a vehicle is given by C=2V + 392/V, where, V= the average speed of the vehicle. Find the speed which will give the cheaps trip. Worth 3 marks out of a shitload (probably 100, cant remember)
Simple question, all you do is differentiate C, find the minimum point, SO....
I differentiated C, and got....... C'= 2 + 392 {my error lies here, differentiate first term, integrate the second.......SHIT, maybe I should join general now}
but, that doesnt let me find the minimum turning point, it just gives me a constant, wtf?
So, after decided I was correct and the exam must be wrong, decided to try make C=0 and solve for V.
2V^2=-392,
V^2=-196,
V=14i,
test V=14, C=56
V=13, C=56 + 2/13
V=15, C= 56 + 2/15
so, V=14, cheapest trip
COMPLETELY INCORRECT, BUT CORRECT ANSWER.
It was about 2 minutes after walking from the exam that I realized I integrated and messed up doing the correct, first method with C'. I'm so embarrassed about the stupidness of my mistake, but, did I invent a new way to solve the question, or is it just a fluke ended up with the right answer?
We'll have to wait see what my teachers get out of it. I'm devastated that I threw out the bit of paper with my C'=... attempt, so now they'll just think I didnt know how to do the question, when I really did, just screwed up. STAPLE ALL WORKING OUT EVEN IF ITS SCRAP TO THE EXAM, IT COULD HAVE MARKS, EVEN IF YOU THINK YOU'RE WRONG!!!! I learnt the hard way!