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Mathematics
Problem
If
z
=
1
2
−
2
i
z = \frac{1}{2} - 2i
z
=
2
1
−
2
i
is such that
∣
z
+
1
∣
=
α
z
+
β
(
1
+
i
)
|z + 1| = \alpha z + \beta (1 + i)
∣
z
+
1∣
=
α
z
+
β
(
1
+
i
)
,
i
=
−
1
i = \sqrt{-1}
i
=
−
1
and
α
,
β
∈
R
\alpha, \beta \in \mathbb{R}
α
,
β
∈
R
, then
α
+
β
\alpha + \beta
α
+
β
is equal to (2024 Main, 29 Jan III) (a) -4 (b) -1 (c) 2 (d) 3
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