SUMMARY
The radius of convergence for the power series of the function 1 / (z - 1), expanded about the point z = i, is determined to be sqrt(2). The discussion emphasizes the importance of correctly identifying the center of the series expansion, which in this case is z = i, rather than z = 0. The Ratio Test is applied, confirming that the only singularity affecting convergence is at z = 1, which is sqrt(2) units away from the center.
PREREQUISITES
- Understanding of power series expansions
- Familiarity with the Ratio Test for convergence
- Knowledge of complex analysis, specifically functions of a complex variable
- Ability to manipulate algebraic expressions involving complex numbers
NEXT STEPS
- Study the application of the Ratio Test in more complex series
- Explore the concept of singularities in complex functions
- Learn about Taylor and Laurent series expansions
- Investigate convergence criteria for power series in complex analysis
USEFUL FOR
Students and educators in mathematics, particularly those focused on complex analysis and series convergence, as well as anyone preparing for advanced calculus or analysis courses.