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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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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 equati ...
Okay, so you know it's an arc of a circle, that's good. Hopefully you've drawn yourself an Argand diagram.
Your goal is now to find the center and radius of the circle.

Hint: angle at center = 2 x angle at circumference is _very_ useful here.

I'll let you fill in the intermediate steps.

The last step is to determine a range of x or y, so to limit the entire circle to just the required arc.

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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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