VCE Specialist 3/4 Question Thread!

[Hancock]

So Null-Factor law states that either or










Therefore the solutions for the system is:


I think I know what you did. You can't divide by on both sides of the equation because it just so happens that cos(t) = 0 in our solution set. Since you can't divide by zero, you lost some solutions and it screwed up from there. It's always better to do factorization when you are dealing with functions to avoid this problem. It's also noted in the study design (or recap) for 2011.

[Homer]

Yes you're right Hancock, haha i did divide by cos(t) and only obtained cos(t)=+or-1. Thanks again

[Hancock]

No problems bud, keep the questions coming haha.

[Homer]

if z=1+i find z^4

I know I could work it out by multiplying (1+i)(1+i)(1+i)(1+i). Is there any other method I could use?

[Stick]

Have you learnt De Moivre's theorem?

[Homer]

so would i need to convert it into polar form?

[Stick]

Yes, that would be it. 1+i is fairly straightforward (I just know it by heart lol).

[Homer]

yeee ive got the answer using de moivre's theorem, but this question was like 2 exercise before the one where we learn the theorem, so I thought there would be a different method :/

[b^3]

Convert into polar form, apply de'movires theroem, solve it back out.

Spoiler

 

EDIT:

yeee ive got the answer using de moivre's theorem, but this question was like 2 exercise before the one where we learn the theorem, so I thought there would be a different method :/

In that case, if you didn't know it then yeh, expand it out, then it should come to the same result, although once you know de'movires, its better to stick with it.

Spoiler

[pi]

yeee ive got the answer using de moivre's theorem, but this question was like 2 exercise before the one where we learn the theorem, so I thought there would be a different method :/

Haha, just use the method you would use in an exam Which is to use De Moivre's theorem as you did

[Stick]

If that's the case, you'd probably just have to expand it normally. Using Pascal's Triangle might speed things up though.

[Homer]

haha yeah coz THEN the question asks us to find out z^12. This would take like forever considering de moivre's theorem is 2 exercise away and we aren't supposed to know it yet. Maybe it wants us to work things out on the calculator? :/

but thanks anyways guys

[Stick]

Yeah, it might be a good idea to practice your calculator skills then.

[pi]

haha yeah coz THEN the question asks us to find out z^12. This would take like forever considering de moivre's theorem is 2 exercise away and we aren't supposed to know it yet. Maybe it wants us to work things out on the calculator? :/

but thanks anyways guys

Well, not really

If (1+i)^12 = ((1+i)^4)^3 = (-4)^3 = -64

I plucked (1+i)^4 out because it was in the previous part of the question

[Homer]

smarty pants