ATAR Notes: Forum
HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 2 => Topic started by: 006896 on December 19, 2018, 11:33:57 am
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Hi,
A question asks to find locus of z when Re(z-(1/z))=0. I have found that the locus is x=0 and x^2+y^2=1. What does this mean? Which locus is it? It is both loci at the same time, or either locus independently? Or is the locus where the two equations intersect?
Thanks
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The locus incorporates both of those regions. Only one of those conditions needs to hold (i.e. \(x=0\) or \(x^2+y^2=1\)), but that consequently means that both of them are plotted on the Argand diagram.
In your computations, with careful rearranging you should be able to obtain that \(x (x^2+y^2-1) = 0 \). Recall that the solution to this is that \(x=0\), OR \(x^2+y^2-1 = 0\), i.e. only one of them needs to equal zero.
(Although, note that the locus excludes \(z=0\), i.e. the point \((0,0)\).)