If $z = \frac { 1 } { 2 } - 2 i$, is such that $| z + 1 | = \alpha z + \beta ( 1 + i ) , i = \sqrt { - 1 }$ and $\alpha , \beta \in \mathrm { R }$, then $\alpha + \beta$ is equal to (1) - 4 (2) 3 (3) 2 (4) - 1
If $z = \frac { 1 } { 2 } - 2 i$, is such that $| z + 1 | = \alpha z + \beta ( 1 + i ) , i = \sqrt { - 1 }$ and $\alpha , \beta \in \mathrm { R }$, then $\alpha + \beta$ is equal to\\
(1) - 4\\
(2) 3\\
(3) 2\\
(4) - 1