已知z^2+49/z^2是实数,求复数z在复平面上对应点集的图形

令z=x＋iy,则z^2＋49/z^2=x^2-y^2＋i2xy＋49(x-iy)^2/[(x＋iy)^2(x-iy)^2]=x^2-y^2＋i2xy＋(49x^2-49y^2-i98xy)/(x^2＋y^2)^2,令上式虚部为零,即2xy-98xy/(x^2＋y^2)^2=0,即2xy=98xy/(x^2＋y^2)^2①；如果xy≠0,则①式变为x^2＋y^2=7②；另外x=0或y=0也满足①式(x、y不能同时为零,否则z^2不能做分母)；综上所述,z在复平面上对应点集的图形为：除去原点的坐标轴和圆x^2＋y^2=7.