An algebra problem by Madhavan V

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 $| y_1|+| y_2 |= ?$

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