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Let x(1),x(2) are the roots of the quadr...

Let `x_(1),x_(2)` are the roots of the quadratic equation `x^(2) + ax + b=0`, where a,b, are complex numbers and `y_(1), y_(2)` are the roots of the quadratic equation `y^(2) + |a|yy+ |b| = 0`. If `|x_(1)| = |x_(2)|=1`, then prove that `|y_(1)| = |y_(2)| =1`

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To solve the problem, we need to prove that if \( |x_1| = |x_2| = 1 \), then \( |y_1| = |y_2| = 1 \) for the given quadratic equations. Let's go through the steps systematically. ### Step-by-Step Solution: 1. **Identify the roots of the first quadratic equation**: The roots \( x_1 \) and \( x_2 \) are the solutions to the equation: \[ x^2 + ax + b = 0 ...
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