解决数学问题总是从观察与联想开始.通过观察,对问题产生一定的感性认识.进而对问题展开广泛的联想,从而探索出解决问题的途径.现对一例进行观察与联想. 问题已知z为非零复数,z+4/z∈R,且|z-2|=2,求z. 看到z+4/z∈R这个条件可联想到什么呢?z+4/z的共轭复数是它的本身,即z+4/z=z+4/z,从而得z2(?)+4(?)=z(?)2+4z.看到|z-2|=2可联想到什么呢?点Z的轨迹是点 Solving mathematics problems always begins with observation and association. By observing them, they have a certain perceptual knowledge of the problem. Then they expand their association with the problem and explore ways to solve the problem. Now we observe and associate an example. Problem Known For non-zero complex numbers, z+4/z∈R, and |z-2|=2, find z. What does the condition of z+4/z∈R think of? Conjugation of z+4/z The complex number is itself, ie, z+4/z=z+4/z, so that z2(?)+4(?)=z(?)2+4z. Seeing |z-2|=2 is associable What is it? Point Z’s trajectory is the point