Here $$|z - 3| < 1$$

$$ \Rightarrow {(x - 3)^2} + {y^2} < 1$$

and $$z = (4 + 3i) + \overline z (4 - 3i) \le 24$$

$$ \Rightarrow 4x - 3y \le 12$$

$$\tan \theta = {4 \over 3}$$

$$\therefore$$ Coordinate of $$P = (3 - \cos \theta ,\sin \theta )$$

$$ = \left( {3 - {3 \over 5},{4 \over 5}} \right)$$

$$\therefore$$ $$\alpha + i\beta = {{12} \over 5} + {4 \over 5}i$$

$$\therefore$$ $$25(\alpha + \beta ) = 80$$