An algebra problem by Madhavan V

Algebra Level 3

Let $x_1,x_2$ be the roots of the quadratic equation $x^2+ax+b=0,$ where $a$ and $b$ are complex numbers, and $y_1,y_2$ are the roots of the equation $y^2+| a |y+| b|=0$ .

If $| x_1 |=| x_2 |=1,$ what is $| y_1|+| y_2 |= ?$

Note: $| \cdot |$ denotes the absolute value function.