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JEE Math Practice Question

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

  1. A.2
  2. B.$$-$$4
  3. C.3
  4. D.$$-$$1

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