Parametrizing a Circle: Solving |z-z_o| = r for z(t)

Thread starter squaremeplz
Start date May 7, 2009
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Circle

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To parametrize the circle defined by |z - 2 + i| = 3, the correct center is identified as 2 - i. The proposed solution is z(t) = 2 + i + 3e^(it), but there is uncertainty regarding the center's position. The adjustment to z - (2 - i) clarifies the center's location. This leads to the conclusion that the parametrization should be adjusted accordingly for accuracy. The discussion emphasizes the importance of correctly identifying the center in circle parametrization.

May 7, 2009

squaremeplz

Homework Statement

trying to parametrize |z - 2 + i | = 3

Homework Equations

|z - z_o| = r

The Attempt at a Solution

z(t) = 2 + i + 3e^(it)

im not sure if 2 + i is correct, or 2 - i.

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May 7, 2009

Mark44

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z - 2 + i = z - (2 - i), so the center is at 2 - i.
With that change, I think you have what you need.

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