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Orthogonal means at 90 degrees to. Z=\sqrt{\frac{1+z}{1-z}}, \,\, \text{with} \,\, \left |z \right |=1 \\\\ \text{Let} \,\, z=\cos2\theta+i\sin2\theta \\\\ Z=\sqrt{\frac{1+\cos2\theta+i\sin2\theta}{1-\cos2\theta-i\sin2\theta}} \\\\...

Nope

\text{Note that} \,\, 4+3i=i\left ( 3-4i \right ) \\\\ \therefore \frac{\left (3-4i \right )^{5}}{\left (4+3i \right )^{3}}=\frac{\left (3-4i \right )^{5}}{\left (3-4i \right )^{3}\left ( i \right )^{3}} \\\\ = -\frac{\left ( 3-4i \right )^{2}}{i} = -\frac{9-24i-16}{i} \\\\ = \frac{7+24i}{i} = 24-7i

Sorry, that was meant to be: \text{Let} \,\, x^{3}-2-2i=\left [ x-\left ( -1+i \right ) \right ]\left ( ax^{2}+bx+c \right ) \\\\ \text{By equating coefficients,} \,\, a=1 \\\\ 1-i+b=0\Rightarrow b=-1+i \\\\ c\left (1-i \right )=-2-2i \\\\ c=\frac{-2-2i}{1-i}\Rightarrow...

What about SCIF1021? I understand it isn't offered in the next semester - wouldn't it be a good idea to do it in first then?

I'm in exactly the same boat as you, so it's good to hear I'm not alone :) I've currently enrolled in MATH1151, ECON1101, ACCT1501 and SCIF1021. The reason for the last one, is because it's only available in first semester.

Bachelor of Commerce/ Bachelor of Science (Advanced Mathematics) - full time at UNSW Took years to load, hang in there guys :)

You could also do this: \frac{x^3}{x+1} = \frac{x^3+1}{x+1} - \frac{1}{x+1} \\ = \frac{(x+1)(x^2-x+1)}{x+1} - \frac{1}{x+1} \\ = x^2-x+1-\frac{1}{x+1} Pardon me jetblack2007 - my LaTeX isn't working at all =/

\int_{0}^{\frac{\pi}{2}}\frac{\sin x}{\sqrt{1+2\cos x}}dx \\\\ \text{Let} \,\, y=1+2\cos x \\\\ \frac{dy}{dx}=-2\sin x \Rightarrow dx=-\frac{dy}{2\sin x} \\\\ \text{When} \,\, x=\frac{\pi}{2}, \,\, y=1 \\\\ \text{When} \,\, x=0, \,\, y=3 \\\\ \therefore \int_{0}^{\frac{\pi}{2}}\frac{\sin...

Product of roots is -d/a

Post here xD

To each his own buddy =]

Nice! I did this: x^5 + x^4 + x^3 + 1 - x^3 = x^3(1 + x + x^2) + (1 - x)(1 + x + x^2) ===> (1 + x + x^2)(x^3 + 1 - x)

\text{Here's one; factorise} \,\, x^{5}+x^{4}+1

<3

I applaud your patience with LaTeX =] Well done. @ adomad - this is stuff not really learnt in MEII, but it guides you through it quite nicely, so there's no reason why a competent MEII student can't do this. \left ( i \right ) \\\\ 1-r^{2}+r^{4}-r^{6}+r^{8}-...=\frac{1}{1-\left ( -r^{2}...

Beautiful. Also I see there's no solution to that problem yet. I will post one if there's none by 11:30 - started writing yesterday, but there was tons of code.

|x - 5| < 5x + 9 Solve for |x - 5| = 5x + 9 x - 5 = 5x + 9 or/ x - 5 = -5x - 9 x = -7/2 or/ x = -2/3 After testing x > -2/3, -7/2 < x < -2/3 and x < -7/2; you can deduce that x > -2/3

\left ( a \right )\text{Show that} \\\\ \frac{1+\cos\theta+i\sin\theta}{1-\cos\theta-i\sin\theta}=i\cot\frac{\theta}{2} \\\\ \left ( b \right )\text{Let n be a positive integer. Show that all the roots of the equation}\left ( z-1 \right )^{n}+\left ( z+1 \right )^{n}=0 \,\, \text{can be written...

Bear in mind that it's only early for '10ers - they would most probably be up to conics now =] There do exist some interesting conics questions, there was one I posted a solution for a while back which was quite unusual.