Adding/subtracting in polar coordinates?

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Discussion Overview

The discussion revolves around the addition and subtraction of quantities in polar coordinates, specifically addressing the challenges and methods involved when not converting to rectangular coordinates. The context includes mathematical reasoning related to complex numbers expressed in polar form.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks how to add or subtract in polar coordinates without converting to rectangular coordinates.
  • Another participant suggests converting to rectangular coordinates for addition or subtraction, then converting back to polar coordinates.
  • A different participant questions the premise by noting that coordinates apply to points, implying that addition or subtraction may not be appropriate unless discussing vectors, which require defining basis vectors.
  • A later reply clarifies that the original inquiry was about adding complex numbers in polar form, indicating a specific context for the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of adding or subtracting in polar coordinates, with some suggesting conversion to rectangular coordinates while others challenge the premise of such operations without defining the context (points vs. vectors).

Contextual Notes

There is ambiguity regarding the definitions of the quantities being added or subtracted, particularly whether they refer to points or vectors, and the implications of using basis vectors in polar coordinates are not fully explored.

coregis
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How do you add or subtract in polar coordinates if not given the rectangular coordinates? Thanks.
 
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Convert to rectangular coordinates then add/subtract. Convert back to polar coordinates.
 
Adding and subtracting what? Coordinates apply to points and you don't add or subtract points. If you are talking about vectors, then you will have to establish what you "basis" vectors are. In Cartesian coordinates, you can take the unit vectors in the x y directions as basis vectors. You can't do that in polar coordinates.
 
Thanks. I thought that was the only way to do it. Sorry for not being so clear. I was trying to add complex numbers in the polar form.
 

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