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.

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