Bazza's 3/4 Question Thread

[WhoTookMyUsername]

1) What is rectangular mode on the CAS?
2) Difference with polar?
3) When should we use and not use it?
4) What's the best way to approach questions such as ?
Is it to remember that i^4 = 1 and then cancel down and remember that               etc? (best to learn these off by memory?)

[paulsterio]

1) What is rectangular mode on the CAS?
2) Difference with polar?
3) When should we use and not use it?
4) What's the best way to approach questions such as ?
Is it to remember that i^4 = 1 and then cancel down and remember that               etc? (best to learn these off by memory?)

1) - Rectangular is a+bi form
2) - Polar, in VCE, is rcis(theta) form, but can also be e^(i*theta)
3) - What do you mean when should we use and not use it? Depends on the question?

This is how I would do 4)

[WhoTookMyUsername]

thanks paul, just with the last one how did you get from to 1 ?
Like what mental process did you follow specifically?

thanks

[Lasercookie]

thanks paul, just with the last one how did you get from to 1 ?
Like what mental process did you follow specifically?

thanks

1 multiplied by itself 503 times is just 1

[Phy124]

thanks paul, just with the last one how did you get from to 1 ?
Like what mental process did you follow specifically?

thanks

1 to the power of any number = 1?

edit: never mind laseredd beat me to it

[paulsterio]

Oh and also, just for the reference

If is even,



If is odd,

[WhoTookMyUsername]

The textbook is giving me mixed messages
in some places it suggest cartesion form is better as

(factorised) and in other places suggest something like is better. Generally which is the best way to represent it? (is this the same when ugly fractions can be factorised out?)

thanks

[paulsterio]

Both are ok, but I would say to use 2+2i, the other form is just unneccesarily confusing

All forms are ok unless a specific form is required, this is usually always true, for example, 2(i+j+k) is as acceptable as 2i+2j+2k

[WhoTookMyUsername]

thanks paul, couple more questions

1) if it says "express in the form x + yi" then is 2+2i better?
2) In year 11 we were taught to the arg(z) before quadrant was taken into account as A (alpha). Is this notation OK in year 12?

[paulsterio]

1) If it says x+yi, then yes, I would definately expand

2) Hmmm, I don't know if the notation is ok or not, but i'd just say let "alpha" = arg(z) and then go on to do the working, if you define it, it's defs ok.

[WhoTookMyUsername]

yeah i think with 2) i'll just go arg(z) = ... or pi - ... etc.

[WhoTookMyUsername]

another "form" type quetions. If i'm asked to express in the form x + yi / cartesian form

and there's a 0 or 0i , do i write that down?

(e.g. 0 + i, 1 + 0i)?

2) is sina okay ? or is sin (a) preferable (do they take off marks for the former?)

[monkeywantsabanana]

another "form" type quetions. If i'm asked to express in the form x + yi / cartesian form

and there's a 0 or 0i , do i write that down?

(e.g. 0 + i, 1 + 0i)?

2) is sina okay ? or is sin (a) preferable (do they take off marks for the former?)

No you just write the imaginary or real where they exist.

--> 0+i = i

I've been writing my trigs with and without the brackets whenever i feel like it... I don't think it's a big problem as long as it's clear

[paulsterio]

Hmmm, if you're asked to put it in form, this is what I have to say. You can technically put but it really doesn't hurt to put - you don't lose anything and it's guaranteed to be accepted.

Similarly with the trigonometric functions, why would you leave out the brackets? - Marks won't be taken off, I don't think, but it's not much of a hassle to put in brackets, so do that, plus it's a good habit, it makes things clearer

[WhoTookMyUsername]

I have no problems with partial fractions problems ATM but i am having a slight bit of trouble understanding a princple. When you have something like i can see why one resultant fraction is a  "linear" ( can i call it this ) and one is a contant; but ehy is something like not also in this form? Why are both resultant factors constantr? I dont really understand atm, please explain .


Thanks