Complex Analysis: Theory and Applications · Problem 4.4.6

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · power-series-convergence-existence

Problem

Does there exist a power series

\displaystyle\sum_{n=0}^{\infty} c_n z^n

that converges at

z_1 = 4 - i

and diverges at

z_2 = 2 + 3i

? Why or why not?