If $\mathrm{z}=\frac{1}{2}-2 \mathrm{i}$, is such that $|\mathrm{z}+1|=\alpha \mathrm{z}+\beta(1+\mathrm{i}), \mathrm{i}=\sqrt{-1}$ and $\alpha, \beta \in \mathrm{R}$, then $\alpha+\beta$ is equal to
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