Help! I'm really getting myself into a mess at school, with every subject even maths/further maths.
I went for help from my teacher today and she did nothing but totally confuse me, telling me contradictory stories, making no sense whatsoever. The topic of "what is the square root of 9" "It is 3" came up. The true answer to this surely is "plus or minus 3" and she said "no, just 3, since functions aren't many-to-one mappings"....to which I replied "but we aren't dealing with functions!". She confused me totally, saying things like there are NO roots to a quadratic when the determinant (b^2-4ac) is less than 0...but I said there are...root -4 is 2i. I say this since we're dealing with complex numbers (EdExcel P6) right now but she said there are NO roots unless you are working in the complex plane.
Anyone with a P6 text book, help me! What is the modulus of something, I was always taught it was to make it positive. Now I'm being told different, that it's a length! Everything is changing now!?! This is horrible!
P6, page 44. My maths teacher said that vectors cannot be numbers, since they are scalars - yet then she said on page 44, think of these Z1's as lengths of lines AND vectors, which, again, contradicts!
I can understand if we had just z1 and z2, then the result, OQ on that diagram, would be z1+z2 (providing z1 and z2 are vectors). But now, we have modulus signs round them which mean lengths! So we have modulus z1 as the line OP, and modulus z2 as the line PQ, so modulus (z1+z2) for the line OQ. This makes no sense!!! Surely if this means they are lengths, then how can a) they be vectors and how can the diagonal line OQ be z1+z2!?
One last thing, we were always taught the cube root of 1 is 1. Now we're taught it is some strange thing such as cos 2pi/3 + i sin 2pi/3. When i asked my teacher about it today, she said "Of course it's just 1, there's no other roots"....and i said "BUT YOU'VE JUST TAUGHT US IT HAS 2 OTHER ROOTS" and she said "you don't say those, the cube root of 1 is just 1 and always will be 1...just like the square root of 4 is ONLY 2." But I have been taught it is -2 aswell. Why is she contradicting herself?!
This arose after doing a question after chapter 2.5 in complex numbers where we learnt there is more than 1 root, then we did an example, which, during the example, involved us taking the cube root of 'r', which was 1. She said the cube root of 1 was just 1...AFTER WE HAD JUST BEEN TAUGHT IT HAS 2 OTHER ROOTS!
I'm getting totally fed up of her contradicting herself and not explaining herself very well! Teachers are always too bloomin' busy for asking for help. I have been "queued" for help for a week and a half now, and saw her for 40 minutes, and she solved NO PROBLEMS i had, in fact, made them worse.
Someone help me please! I feel terrible right now...angry, furious, depressed, stressed, annoyed and any other vulgarities one can think of. I need a punch bag! ARGH!
Modulus means the magnitude or size or length of something eg l-3l = 3 because if you draw a line from 0 to -3 it has magnitude/ length 3. In terms of complex numbers, the complex number z1 can be represented by a vector in the complex plane from the origin to a point P. The length of the line is the modulus of z1 = lz1l. So if you have the vectors in the complex plane shown by z1, z2 and z1 + z2, the length of these lines is the modulus of the complex number.
About the roots of equations there are many roots because the squareroot is not strictly a function because it does not provid a one to one mapping of reals. In fact nth roots have n solutions. However for convenience and logistic sense we often take only one of the possible values eg if v = 1 - t^2 where v is velocity and t is time, when is v = 0. Well in algebra t = +/- 1 but we only take t = 1. Similarly when z = re^ix and we want to find, say z^1/3 we only take the real and if possible positve value of r^1/3.