I need help with this problem.

Problem ID. Let Hz] be an entire function. Assume that there exists a complex number an. and a positive number E such that \"{2} nal 2} E 3} [l for every 2 E III {in other words? the image of ffz) misses a neighborhood of 2.3.). Show that z} ie a constant. In other words... the image of a nonconatant entire function come; arbitrarily close to any complex value