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[M2] Please help locus question

Please help locus question

I have no idea how to really do this question at all

I separated it into Arg(z-1) - Arg(z+1) = pi/4 and I realise that the locus is an arc of a circle, but not sure how to find the cartesian equation.
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回覆 2# 風之男 的帖子

Thank you very much for your help, I think I solved it; I drew the argand diagram, and the angle at the centre of the circle is 90º. Then I can form a right angled isosceles triangle with the hypotenuse length 2 and so the shorter sides must be sqrt2.

Sorry, I don't have the answer for it, can I ask you to confirm my answer of the equation being x^2+(y-1)^2=2 ?

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