Search results

Re: HSC 2013 4U Marathon Maybe you can use the fact that |z|^2 = z zbar...

Re: HSC 2013 4U Marathon Long time no see. Out of the closet?

Apparently Bio is all memorising and can be picked up very easily later if needed.

Re: HSC 2013 4U Marathon Are you using LaTeX?

Re: HSC 2013 4U Marathon There's another way to do this problem using mappings in complex analysis. It's WAY more elegant. EDIT: Here is my sketch solution: Let 'c' be the complex number representing centre of the circle. Then the equation of the circle is |z-c| = |c| (since the circle...

Re: HSC 2013 4U Marathon I think an 'elegant' approach to this is setting one of the points to 0, finding a condition and then using a change of coordinates.

Re: HSC 2013 4U Marathon Yeah. Typo haha. And I think I fixed the formatting now.

Re: HSC 2013 4U Marathon In most cases yes. But for my example, geometrically speaking, |z-i| + |z+i| is the sum of the distances from any point z to the points i and -i. So the minimum value its minimum value will be 2. So, if I'm correct, then the locus of |z-i| + |z+i| = 2 will be the...

Re: HSC 2013 4U Marathon If I'm not mistaken, it is not an elllipse, but a line...

Re: HSC 2013 4U Marathon Spiral!!! :P

Re: HSC 2013 4U Marathon Find the Cartesian equation of the locus for all points z such that |z+i|+|z-i| = 2. Hint: Think before performing "mindless algebra".

3U inequality induction questions are alright. Most of the time you "fudge" the answer to the next step and then justify it in the previous step. There are 4 main types of induction: 1. Summation 2. Divisibility 3. Inequality 4. Miscellaneous (mostly 4U)

Yes they are. They're basically the range of the sin and cos functions.

I think MathType would've been way slower for me :|

Carrot, you should try and learn LaTeX. I believe the HSC paper is written in LaTeX as well (using a package that changes the default font to something that looks like Times New Roman - it isn't exactly that though, since that exact font is patented or something...)

I remember for my actual Ext 1 HSC trial the exam started 8:55am and when I had finished Q1 the time was 9:00am, and I got full marks for Q1.

Nice, but some of the questions seem a bit too long for a MC question.

Lol, yeah that is cool. There's two ways of actually doing that. Method 1: Use the fact that sin z = [e^(iz)-e^(-iz)]/(2i) and solve the resultant quadratic Method 2: Use sin(x+iy)=sinx cosh y + i cosx sinh y. But this method only works if the imaginary or real part is zero.

Re: MX2 Integration Marathon Lol, wallis product... nice :P

Re: MX2 Integration Marathon Haha, complex analysis is really really nice. How's Peter Brown? Gotta love how he personifies maths :P