How can I transform a line in the z plane to a circle in the w plane?

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SUMMARY

The discussion focuses on transforming a line in the z-plane to a circle in the w-plane using complex analysis. The key transformation involves mapping the unit circle |w|=1 to a circle centered at 3-i with a radius of 2. Participants emphasize the importance of utilizing the initial transformation derived in part a to complete the task effectively.

PREREQUISITES
  • Understanding of complex numbers and the z-plane
  • Familiarity with transformations in complex analysis
  • Knowledge of circle equations in the complex plane
  • Experience with mapping techniques in mathematical analysis
NEXT STEPS
  • Research the concept of conformal mappings in complex analysis
  • Study the properties of circles in the complex plane
  • Learn about transformations that map circles to other circles
  • Explore the use of the Riemann mapping theorem for complex transformations
USEFUL FOR

Mathematicians, students of complex analysis, and anyone interested in geometric transformations in the complex plane.

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Just find the transformation that maps the circle |w|=1 into into the circle around 3-i of radius 2. Then you can use a) to finish it.
 


Thank you very much!
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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