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For part a) x-(a+b+c) is the root P(a+b+c) = (a+b+c-a)(a+b+c-b)(a+b+c-c) - (b+c)(c+a)(a+b) = (b+c)(a+c)(a+b) - (b+c)(c+a)(a+b) = 0 For part b) Factorising P(x) = (x-2)(x+3)(x+1)-4 Using part a), let a=2, b=-3, c=-1 (corresponding numbers from part a) As x=a+b+c is a...

Same. I have horrible time management :(

For the first question specified: Let z= x+iy l z l = square root of (x^2 + y^2) l z l^2 = x^2 + y^2 x^2 + y^2 + 2i(x-iy) = 4i + 7 x^2 + 2y + y^2 + 2ix = 7 + 4i Equating co-efficients: x^2 + 2y + y^2 = 7 (1) 2ix=4i x= 2 Sub x=2 into (1) y^2 + 2y -3 = 0 (y+3)(y-1) = 0 y= -3, 1 Therefore, z =...

The modulus of z is equal to the square root of a^2 + b^2 (a^2 + b^2)^(1/2) If you were to square the modulus, it would end up as a^2 + b^2 Do you have the answer for the given question?

Is it correct? If we were to tweak the equation, it would appear as: x^2 + y^2 + 2i(x-iy) = 4i + 7 Separate into real and imaginary parts, then equate coefficients to receive the final answer (z=x+iy).

For question two, is the answer z=2+i or z=2-3i

If I were in your circumstance, I would probably drop geography - but then again during junior school, I was an abomination to social science ahaha. Over the holidays you could easily catch up on the significant aspects of chemistry that accumulate throughout the Year 12 course. From what I've...

Ahaha the best feeling. Wow you're very dedicated!

Holidays are coming up soon - I'm quite glad year 11 doesn't count because prelim results were anti-climactic.

I've produced a similar thread however have gotten finalised marks, ranks, etc. however am unsure what subject to drop. I'm opting for either 11-12 units, as I am planning to pick up Mathematics Extension II. School rank: ~300s :P English Advanced: 1/98 English Extension: 1/24...

I just finished prelims too. Year 12 imminently awaits :P

School routine: 3:00pm - Arrives home 3:30pm - Eats a *very* early dinner ahaha 4:00pm - Relax, YouTube, Read 5:00pm - Homework, Studying 7:00pm - News 8:00pm - Homework, Studying 9:00pm - Brushing my teeth, washing face, etc. Reading 10:00pm - Sleeping

Hi there! Wow, you're very keen considering how you're in year 10 yet doing 4u. That's always good to hear. For the first question, z+ (1/z), change z= a + ib a + ib + (1/(a+ib) Multiply 1/(a+ib) with its conjugate to receive: = a+ib + [(a-ib)/a^2+b^2)] Afterwards, multiply a+ib with a^2 + b^2...

Aren't you in year 11 though?

I just realised its ambiguity - did the school purchase the paper or was it drafted by the maths department?

Those are fantastic marks and ranks, especially without tuition! Was your yearly an independent paper?

1) A textbook is by far superfluous; you should be able to integrate your own perception of the text, in conjunction with teacher resources, online notes, etc. 2) Studying for EEI is generally sustained - your teacher will expect you to draft essays and creatives as part of its core component in...

Have they provided you with an answer? I'm not sure whether my answer is correct ;P

Probably around low 80s. Don't be discouraged however given your remaining HSC exams and their bulk in the overall mark.

I'm not really sure - ~96-97 Aren't you still in prelim though? Ranks could easily shift from year 12 onward. Great ranks however!