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Question

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My attempt

$ -\arg(z1/z2)=\arg(z1)-\arg(z2) $

$z1=(x+\alpha)+iy $ and $ z2=(x+\beta)+iy $

$\arg(z1)=\arctan(y/x+\alpha) $ and $ \arg(z2)=\arctan(y/x+\beta) $ ....

But this method is very lengthy. Is there another elegant approach?

Rohit Singh
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Shivanshu Singh
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  • Actually,How to edit I don't know sorry . – Shivanshu Singh Jul 07 '22 at 05:53
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    Welcome to Math SE. To edit, click the Edit link (it should be the third one from the left side, between the "Cite" and "Follow" ones, just below your question). – John Omielan Jul 07 '22 at 06:23
  • May I have the source? Thx – Mikasa Jul 07 '22 at 07:22
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    @ShivanshuSingh look at the complex equation given. This represents an arc of a circle. I think you need to read up on it. – insipidintegrator Jul 07 '22 at 07:30
  • @ShivanshuSingh What is the role of $w$ given in the question? – Sourav Ghosh Jul 07 '22 at 07:33
  • Is $arg(z) =\arctan(\frac{y}{x}) $ always true? – Sourav Ghosh Jul 07 '22 at 07:45
  • @LostinSpace that’s for the sake of definition. – insipidintegrator Jul 07 '22 at 07:58
  • @insipidintegrator: Can you give me detailed solution and analysis of the problem for complete understanding.My method is very calculative and confusing . – Shivanshu Singh Jul 07 '22 at 08:06
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    @ShivanshuSingh https://proofwiki.org/wiki/Equation_of_Circular_Arc_in_Complex_Plane and https://math.stackexchange.com/questions/1102782/complex-number-locus-of-a-point. Read these and then update your post to include further efforts after reading the links. – insipidintegrator Jul 07 '22 at 08:13
  • @insipidintegrator:Can you refer me some books for Geometry of complex number ,Problem solving for Undergraduate level problems,Conic section. – Shivanshu Singh Jul 07 '22 at 10:24
  • Respected,@insipidintegrator:I understand the concept of the problem thanks a lot – Shivanshu Singh Jul 07 '22 at 10:26
  • @ShivanshuSingh see 1. https://math.stackexchange.com/questions/2717220/book-references-about-complex-geometry?r=SearchResults&s=1%7C87.8978 2. https://math.stackexchange.com/questions/3046810/book-recommendation-for-complex-numbers-and-co-ordinate-geometry 3. https://math.stackexchange.com/questions/2768852/can-anyone-suggest-a-book-on-using-complex-numbers-to-solve-geometry-problems?r=SearchResults&s=2%7C81.2568 – insipidintegrator Jul 07 '22 at 12:34

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