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用“取模法”求复平面上点的轨迹,是利用复数求平面上点的轨迹的较简便方法,但因方程f(Z)=g(z)与方程|f(z)|=+g(z)|不等价。一般说,后者所表示的点的集合包含前者所表示的点的集合,所以用“取模法”求点的轨迹时,往往扩大轨迹的范围,初学者最易(?)略这一点,从而出现差错. 例1.求满足z·(?)+a·z+(?)=0(a>0,z(?)0)的点z的轨迹方程。[错解] 由题设得z(z+1)=-az。
Finding the trajectory of the point on the complex plane using the “modulus approach” is a simpler way to use the complex number to find the trajectory of the point on the plane, but because of the equation f(Z)=g(z) and the equation |f(z)|=+ g(z)| is not equivalent. In general, the set of points represented by the latter includes the set of points represented by the former. Therefore, when the trajectory of the point is calculated by the “modulus method”, the range of the trajectory is often expanded, and the beginner is the easiest (?). As a result, there is an error. Example 1. Find the trajectory equation for point z that satisfies z·(?)+a·z+(?)=0(a>0,z(?)0). [False Solution] The question is set to z(z+1)=-az.