ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: aronno on September 17, 2009, 06:02:29 pm
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Does anyone have a good long set of Questions on complex numbers.
JUST COMPLEX NUMBERS. covering all aspects in the complex numbers area.
I need to focus of this.
thanks.
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...perhaps flip to the complex numbers chapter of your textbook? Or get another textbook? Essential should serve you well, particularly towards the back of the chapter where you get the analysis questions.
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Does anyone have a good long set of Questions on complex numbers.
JUST COMPLEX NUMBERS. covering all aspects in the complex numbers area.
I need to focus of this.
thanks.
With Specialist maths complex numbers makes up a tiny bit of it.
In the exams you'll probably get a gift question about manipulating a complex number fraction and in multi-choice I guarentee you'll get those points on an argand diagram.
Doing the 2008 papers is a must!!!
for exam 1: q1, q2 (to certain degree), q4, q6(to a certain degree) - these are easy questions (If you can't do these you'll find getting a good mark fairly hard.
q3 is a hard question if you didn't study vectors. linearly dependence uses this rule:
if I have say a set of vectors
u, v and w; they are linearly dependent iff au + bv + cw = 0 (where a, b, and c are elements of R) where atleast one of these constants does not equal 0
so for an exam lets use 2008's exam:
a = (-3,2,3), b = (-2,-2,1) and c = (m,0,n)
linear dependence also means that one vector is a linear combination of the others, so for simplicity sake you can say that vector c is a linear combination of vector a and vector b, since, you are asked to find a set of linearly dependent vectors and this will give that.
so let c = sa + tb (s,t elements of R)
now you are given that the j component of c must equal 0 and you can see the j components of vector a and b are equal in size and opposite in sign, thus, s = t.
thus:
(m,0,n) = (-3s,2s,3s) + (-2t,-2t,t)
= (-3s - 2t, 0, 3s + t)
therefore:
m = -3s - 2t
n = 3s + t
t = s => 4s = n & m = -5s
thus m/n = -5/4
which is what the answer is.
q5 revolves around you knowing your kinematics, q7 is a gift if you know your statics, q8 is also a hard question and 9 and 10 require a lot of thinking.
Anyway that is my look at the first exam.
The second exam will really test you with what you can do and you will see a lot of stuff that seems foreign. The best way to tackle the second exam is by leaving the first part (multi-choice is all giving an answer if its right you get the mark, wrong no marks - no matter how much thought you put in) to last and doing the second part. This part awards around 80% of the marks and has gift marks hidden, also, if you find a section b question you are really confident with it will allow you to get ready to really tackle the exam and after seeing yourself answer a heap of questions your confidence will really go up and you'll see hard stuff that you normally would find tricky and this confidence will stop you from fearing those dreaded problems.
Anyway good luck with your exams and I really wished that I heard of this site last year when I was doing VCE.