pi's Specialist Maths Questions

[pi]

Instead of making a new thread for everything, I'll just make one thread. Any help with any of the question I post throughout the year will be much appreciated.

Question:


The problem I have is getting rid of .

Thanks.

[TrueTears]

...1

...2



Solve both equations 1 and 2 for and , square them and the rest is obvious.

[pi]

^^ Thats genius! Makes it look so easy now.

Thanks TT!

[pi]

This is more of a 'can we do this' question. In tests/SACs/exams, are we allowed to use instead of ?

[Mao]

This is more of a 'can we do this' question. In tests/SACs/exams, are we allowed to use instead of ?

There is an appeal to use Euler's form over cis (i.e. the operations actually make sense). I would be careful though. Not every specialist teacher remembers maths beyond what is taught at specialist, and we cannot guarantee every exam marker can recognise higher concepts such as this. The safer thing is to stick with cis.

If you want to use Euler's form, be extra careful and make sure you define it when you use it. i.e.


then proceed with workings.

[pi]

Okay, I think I'll just stay safe with , just in case I forget to define it (then I might be screwed).

Thanks Mao!

[pi]

noob question alert!

Could someone please show me how to find the and intercepts of ?

I can't seem to get a Cartesian equation out of it either (and MQ have no such problems/examples). I can do basic ones like:


, etc (solve for y and then find intercepts -although none in this case)

But am having trouble with finding Cartesian equations and intercepts of rays with translations.

Thanks 

[Bonifacio]

Wouldn't z=x+yi

Therefore tan 2pi/3 = y+3/x-2 then solve from there?


tan 2pi/3 = -√3

-√3 (x-2) -3 =y then make x and y zero when necessary to find intercepts?

[Greatness]

Perhaps you could sub in z= x +iy into the equatoin? And they could be translations??

[pi]

Wouldn't z=x+yi

Therefore tan 2pi/3 = y+3/x-2 then solve from there?


tan 2pi/3 = -√3

-√3 (x-2) -3 =y then make x and y zero when necessary to find intercepts?

Ahhh, I think that makes sense! Can anyone else concur?

[luffy]

Just stating the answer more clearly:



let z = x + yi (i.e. Re(z) = x and Im(z) = y)










i.e.

For the Re(z) intercept, Im(z) = 0.






i.e. Re(z) intercept at

For the Im(z) intercept, Re(z) = 0.



i.e. Im(z) intercept at

There you go (Hope I didn't make any mistakes)

[pi]

Thanks Bonifacio, Water and luffy! No mistakes either

[pi]

I need an easy way for this:


I used and then finding and expanding by making two equations:

and then expanding using Newton's generalised binomial theorem (its big)

Then collecting like terms (ie. those with and those without) and getting the answer.


Any easier ways?


EDIT:
Saw this on Wikipedia:


Can someone also explain this? (I am not familiar with this notation...)


Thanks in advance!

[brightsky]

http://www.trans4mind.com/personal_development/mathematics/trigonometry/deMoivre.htm

[pi]

http://www.trans4mind.com/personal_development/mathematics/trigonometry/deMoivre.htm

Great link brightsky! Thanks