Complex Circles: Path of |z-i| = pi

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SUMMARY

The discussion centers on the geometric interpretation of the equation |z - i| = π in the complex plane. It is established that this equation represents a circle with a center at the point i (0, 1) and a radius of π. The confusion regarding the center being π is clarified, emphasizing that the distance from the variable point z to the fixed point i is π, confirming the circular nature of the graph.

PREREQUISITES
  • Understanding of complex numbers and the complex plane
  • Familiarity with the concept of distance in the complex plane
  • Knowledge of basic geometric shapes, specifically circles
  • Ability to interpret mathematical equations graphically
NEXT STEPS
  • Study the properties of circles in the complex plane
  • Learn about transformations of complex functions
  • Explore the implications of distance equations in complex analysis
  • Investigate the geometric interpretations of other complex equations
USEFUL FOR

Students studying complex analysis, mathematicians interested in geometric interpretations, and educators teaching concepts related to the complex plane.

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Homework Statement



I'm not sure how the graph looks like for the path |z-i| = pi

Homework Equations



I know that if the function is |z-i|=1 means a unit circle center at i


The Attempt at a Solution



Does that mean |z-i|=pi is a circle center at pi with a radius of pi?

Thanks
 
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No. Remember that |a- b| is the distance from a to b in the complex plane. |z- i| says that the distance from the variable point z to the point i is pi. Yes, that's a circle. What is its center?
 

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