I am reading a complex analysis book and have a question about a complex function that the book talks about. Let $z$ and $v$ be complex numbers. Then, the book states that a translation function $T_v(z) = v+z$ and Rotation function $R_a^\theta(z) = e^{i\theta}z$. They also have inverse functions $T_v^{-1}$ and $R_a^{-\theta}$. The book satates that

A rotation of $\alpha$ about the origin followed by a translation of $v$ can always be reduced to a single rotation: $T_v \circ R_0^{\alpha}=R_c^{\alpha}$ where $c=\frac{v}{1-e^{i \alpha}}$.

Since $c$ represents the center of rotation, how can I get the center?? And how can I interpret that center geometrically??

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