Question 7
Let $a$ and $b$ be two complex numbers. Prove that the following statements are equivalent:
1) The absolute values of the roots of the equation $x^2 - a x + b = 0$ are respectively equal to the absolute values of the roots of the equation $x^2 - b x + a = 0$.
2) $a^3 = b^3$ or $b = \bar{a}$.
1) The absolute values of the roots of the equation $x^2 - a x + b = 0$ are respectively equal to the absolute values of the roots of the equation $x^2 - b x + a = 0$.
2) $a^3 = b^3$ or $b = \bar{a}$.