You can definitely solve it that way, but if the marker is strict, you may not receive full marks for not using the directive "hence".
To do (ii), since you showed that -2i is a root of z^3-8i=0, it follows from the Factor Theorem that (z+2i) is a factor.
Therefore z^3-8i=(z+2i)(z^2+Az-4) ...
The graph of a locus represents all the possible points that satisfies a given equation.
You have to exclude (a,0), as it lies on the circle.
Otherwise, you are saying that z=a satisfies Re(z-ib/z-a)=0, which is false.
MATH3969 - Measure Theory and Fourier Analysis (Advanced)
Semester 2, 2016
Ease - 0/10
By far the HARDEST math unit you'll do. If you thought MATH2962 or MATH3961 were even in the SLIGHTEST bit hard, then you my friend are in for one hell of a ride. Do NOT expect going in to this unit of study...
To be honest, probably not. I do not recall any material needed from math1003 (though you should be familiar with how to at least integrate easy functions!). I believe the best preparation for this course is being comfortable with linear algebra, and perhaps some math1001/math1901.
Re: Semester 2 USYD Chatter Thread
That's some great info. Can you comment also on other third year math subjects that you've done? That would be nice.