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A poorly written question is always unfortunate. When it comes to writing complex analysis problems I always feel that geometry should be forced to provide elegant proofs for deep results, not difficult proofs for trivial results. Presumably part c) is the point of the question and unfortunately...

It's always nice to use geometry but it is unfortunate that the question is so ham-fisted. Parts a) and b) are heavy machinery to get to a trivial result. A simple direct algebraic approach for c) is: c) Divide top and bottom by z1 and let w=z2/z1. Then (1+w)/(1-w)=2i. Just solve for w. Still...

Not sure this hangs together properly? When you say z^4+1=(z^2-root2z+1)(z^2+root2z+1) this is a factorization of a polynomial. It is an identity true for every complex z. Suddenly in the next line you are assuming that |z|=1? For example if z=7 then most certainly 49+1/49 is not...

That is the end of Adoculus activities for 2018. Prize was posted today. Thanks to all entrants.

Hi all In Q16 you attempt to use the converse of the equal intercept theorem. This converse does not hold. Just a few sketches will convince you that equal ratios of intercepts does NOT imply that the three lines are parallel. Fortunately it is given that the lines are parallel Cheers

Yep 1/9 seems right.Could you post a png of the question and also the paper and the year thanks.

Nice question Just use the formula in a) with p=3 to yield q=plus or minus 2 This means that y=x^3-3x+2 and y=x^3-3x-2 both have double roots....ie max or min situated at the x axis Sliding y=x^3-3x+2 down 2 units gives a stationary point for y=x^3-3x with a y-value of -2. Similarly for the other

We have reached 50 submissions to the Ad Oculus Extension 2 Mathematics competition and first prize is still up for grabs. Do you use the next three weeks to post a perfect solution or do you jump in early and claim the highest mark? Remember that there is nothing so deceptive as the obvious...

Now that the trials are done welcome to the 2017 Ad Oculus H.S.C. Extension 2 Mathematics Competition. First prize is a beautiful new black Sydney University coffee cup with a $50 bonus for any entrant achieving full marks of 30/30. In the event that the $50 is not won in 2017 the prize will...