(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What is the locus given by

[tex]z(\overline{z}+2)=3[/tex]

where the overbar means conjugate.

2. Relevant equations

3. The attempt at a solution

After using z=x + yi and expanding the backets, one gets the equation:

[tex]x^2+2x+y^2+2iy=3[/tex]

or

[tex](x+1)^2+y^2 +2iy=4[/tex]

which is a circle crossed with the line y=0, which means that the locus is actually the points +/-1. However, the book says it is a circle.

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# Homework Help: Locus with complex numbers

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