[题目]设复数z＝2m+(4-m2)i.当实数m取何值时.复数z对应的点:(1)位于虚轴上?(2)位于一.三象限?(3)位于以原点为圆心.以4为半径的圆上? 题目和参考答案——青夏教育精英家教网—

题目内容

【题目】设复数z＝2m＋（4－m2）i，当实数m取何值时，复数z对应的点：

（1）位于虚轴上？

（2）位于一、三象限？

（3）位于以原点为圆心，以4为半径的圆上？

【答案】（1）m＝0（2）m＜－2或0＜m＜2（3）m＝0或m＝±2

【解析】（1）复数z对应的点位于虚轴上，则m＝0.

∴m＝0时，复数z对应的点位于虚轴上.

（2）复数z对应的点位于一、三象限，则2m·（4－m2）＞0m（m－2）（m＋2）＜0m＜－2或0＜m＜2.

∴m＜－2或0＜m＜2时，复数z对应的点位于一、三象限.

（3）复数z对应的点位于以原点为圆心，以4为半径的圆上，则|z|＝＝4m＝0或m＝±2.

∴m＝0或m＝±2时，复数z对应的点位于以原点为圆心，以4为半径的圆上.

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