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March 28, 2024, 08:52:05 pm

Author Topic: Locus complex numbers question  (Read 915 times)  Share 

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006896

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Locus complex numbers question
« 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

RuiAce

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Re: Locus complex numbers question
« Reply #1 on: December 19, 2018, 11:53:26 am »
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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 \((0,0)\).)