If the equation of the normal to the curve $$y = {{x - a} \over {(x + b)(x - 2)}}$$ at the point (1, $$-$$3) is $$x - 4y = 13$$, then the value of $$a + b$$ is equal to ___________.

Let $$\alpha = 8 - 14i,A = \left\{ {z \in c:{{\alpha z - \overline \alpha \overline z } \over {{z^2} - {{\left( {\overline z } \right)}^2} - 112i}}=1} \right\}$$ and $$B = \left\{ {z \in c:\left| {z + 3i} \right| = 4} \right\}$$. Then $$\sum\limits_{z \in A \cap B} {({\mathop{\rm Re}\nolimits} z - {\mathop{\rm Im}\nolimits} z)} $$ is equal to ____________.

Let $$\alpha_1,\alpha_2,....,\alpha_7$$ be the roots of the equation $${x^7} + 3{x^5} - 13{x^3} - 15x = 0$$ and $$|{\alpha _1}| \ge |{\alpha _2}| \ge \,...\, \ge \,|{\alpha _7}|$$. Then $$\alpha_1\alpha_2-\alpha_3\alpha_4+\alpha_5\alpha_6$$ is equal to _________.

Let $$\{ {a_k}\} $$ and $$\{ {b_k}\} ,k \in N$$, be two G.P.s with common ratios $${r_1}$$ and $${r_2}$$ respectively such that $${a_1} = {b_1} = 4$$ and $${r_1} < {r_2}$$. Let $${c_k} = {a_k} + {b_k},k \in N$$. If $${c_2} = 5$$ and $${c_3} = {{13} \over 4}$$ then $$\sum\limits_{k = 1}^\infty {{c_k} - (12{a_6} + 8{b_4})} $$ is equal to __________.