Bloch's Lemma for the Unit Disc

We prove Bloch's Lemma which is the key tool in proving Bloch's Theorem about the image of the unit disc under a holomorphic function that vanishes at the origin and whose derivative is equal to 1 at the origin. We establish bounds for this function and show that the image of the unit disc contains a small disc centered at the origin. In Bloch's Theorem we will obtain a lower bound on the radius of this disc. #mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #bloch