(no subject)

[mariana]

I am going to fail my FP3 exam... there is no doubt of this. I have been revising all day, I can't do complex numbers and I only just finished matrices. I still have three chapters to go, including vectors (which is going to take me decades) and I don't understand anything I've done yet.

Good thing is - my brain has died, so I'm not even going to notice failing. Bad thing is I'm not sure it's going to recover before Monday, when I have my last exams, which are together, synoptic and Chemistry and therefore a bitch.

I should get back to it, but my headache just won't go away and I keep staring at the page like it's the television screen, as though it's just going to talk me through my revision, which would be wonderful, but alas, has yet to be done properly.

An interactive revision page thingy. That would be cool.

Can anyone teach me complex numbers in the next half hour?

Comments

[chottochigamats.livejournal.com]

www.mathsnet.net might be some help
www.thestudentroom.co.uk has a nice maths forum

Complex numbers:
re^i@ = r(cos@ + isin@)

Useful thing is the expansion of, say, cos5@
(cos5@ + isin5@) = r^5(cos@ + isin@)^5 from de Moivre's theorem, but r=1
= (cos@ + isin@)^5
Then expand using the Binomial Theorem and take only the real elements, as we only want cos@ (you'll need to use sin@^2 = 1 - cos@^2)

Elementary (why call it that? It just makes me feel dumb) transformations from the z to the w planes:
Try to write z in terms of w, then apply the transformations to z necessary to use the identity you've been given, e.g. |z| = 1

Argand Diagram geometry stuff (most of these are fairly obvious given a bit of thinking, alternatively, convert z to x+iy, then demodulusify (good word) both sides):

|z+p+qi| = x : circle of radius x, centre (p,q)
|z+p| = |z+qi| : line bisecting the two points. not sure how to write this down

if any others turn up, convert to x+iy

sinh z = i sin z (I think)
cosh z = cosi z (again, check these)

I hope that's it. Vectors is hell.

[chottochigamats.livejournal.com]

I doubt I could teach it well, I'd get confused and go off on tangents, that's my problem. The exam was ok, but not great. I know I lost a decent number of marks, so I'm not tthinking about it. Are you partying on friday?