LEt $f:\mathbb{D}\rightarrow\mathbb{C}$ be an holomorphic while $\mathbb{D}$ is convex set and let $Ref'(z) >0$ show that for every $z\in D$ $\quad$$f(z)$ is one to one function.
I was thinking on using the cauchy reiman eqations \begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial u}{\partial y}\\-\dfrac{\partial u}{\partial y}&\dfrac{\partial u}{\partial x}\end{bmatrix}
Now this matrix is reversible since $Ref'(z) >0$ and the determinant is not zero. now I wanted to show in some way that $f(z_1) = f(z_2) \rightarrow z_1 = z_2$ I am trying to think how should I use the fact that $D$ is convex set can help me here.
