Problem 1792 (difficulty: 9/10)

Show that domains \(\displaystyle r_1<|z|<R_1\) and \(\displaystyle r_2<|z|<R_2\) are biholomorphic if and only if \(\displaystyle \displaystyle\frac{R_1}{r_1}=\frac{R_2}{r_2}\).

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