If the roots of the equation $x^4-10x^3-50x^2-130x+169=0$ are of the form $a\pm ibandb\pm ia$ and a >b a+b² =then ______

$S_1=x_1+x_2+x_3+x_4=10$
$a+ib+a-ib+b+ia+b-ia=10$
$2a+2b=10$
$a+b=5\to \left(1\right)$
$S_4=x_1{x}_2{x}_3{x}_4=169$
${\left(a^2+b^2\right)}^2=169$
$a^2+b^2=13\to \left(2\right)$
From (1) & (2) ; a = 3, b = 2

$a+b^2=3+4=7$