Show that if \(f:B(0,1)\to \mathbb {C}\) is holomorphic and \(\operatorname {Re}(f'(z))>0\) for all \(z\in B(0,1)\) then \(f\) is injective.
Question
Math 6220 • Complex Analysis
Fall 2024 • Question 5
Question
Fall 2024 • Question 5
Show that if \(f:B(0,1)\to \mathbb {C}\) is holomorphic and \(\operatorname {Re}(f'(z))>0\) for all \(z\in B(0,1)\) then \(f\) is injective.