A simple Complex Analysis Mapping

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SUMMARY

The discussion focuses on solving a complex analysis problem involving the transformation of complex numbers into a circular equation. The initial step involves solving for z + 1 and expressing w in terms of u + iv, followed by rationalizing the denominator to derive (x,y) in terms of u and v. The challenge arises in the second part, where the participant struggles to rationalize the denominator, suspecting that the presence of a constant may indicate a shift in the circle's position. The suggestion to switch to vector analysis is also provided as an alternative approach.

PREREQUISITES
  • Understanding of complex numbers and their transformations
  • Familiarity with rationalizing denominators in complex equations
  • Knowledge of vector analysis as an alternative mathematical approach
  • Ability to interpret equations of circles in the complex plane
NEXT STEPS
  • Study the process of rationalizing complex denominators in detail
  • Explore the geometric interpretation of complex transformations
  • Learn about the equations of circles in the complex plane
  • Investigate vector analysis techniques for solving complex problems
USEFUL FOR

Students and educators in mathematics, particularly those studying complex analysis and geometry, as well as anyone interested in alternative methods for solving complex equations.

NewtonianAlch
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Homework Statement


http://img684.imageshack.us/img684/779/334sn.jpg


The Attempt at a Solution



The first part was fairly straightforward, solve for z + 1, and then get w in terms of u + iv, rationalise the denominator, and then we get (x,y) in terms of u and v, which we substitute back into the equation of the line, and get it into the form of an equation of a circle.

The next part is not as obvious for me, I tried the same method, but I couldn't rationalise the denominator, I'm assuming the circle is shifted somehow because of the 2, but I'm not sure.
 
Last edited by a moderator:
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NewtonianAlch said:

Homework Statement


http://img684.imageshack.us/img684/779/334sn.jpg


The Attempt at a Solution



The first part was fairly straightforward, solve for z + 1, and then get w in terms of u + iv, rationalise the denominator, and then we get (x,y) in terms of u and v, which we substitute back into the equation of the line, and get it into the form of an equation of a circle.

The next part is not as obvious for me, I tried the same method, but I couldn't rationalise the denominator, I'm assuming the circle is shifted somehow because of the 2, but I'm not sure.

If you can't do it with complex numbers, switch to vectors.
 
Last edited by a moderator:

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