Let $\epsilon $ be a positive real number and $a$ a complex number.
Prove the function $f(z)= \sin z +\frac{1}{z-a}$ has infinitely many zeros in the strip $|\mathrm{Im}z| < \epsilon.$
Thanks in advance!
Let $\epsilon $ be a positive real number and $a$ a complex number.
Prove the function $f(z)= \sin z +\frac{1}{z-a}$ has infinitely many zeros in the strip $|\mathrm{Im}z| < \epsilon.$
Thanks in advance!