【題目】設復數(shù)z＝2m＋（4－m2）i，當實數(shù)m取何值時，復數(shù)z對應的點：

（1）位于虛軸上？

（2）位于一、三象限？

（3）位于以原點為圓心，以4為半徑的圓上？

【答案】（1）m＝0（2）m＜－2或0＜m＜2（3）m＝0或m＝±2

【解析】（1）復數(shù)z對應的點位于虛軸上，則m＝0.

∴m＝0時，復數(shù)z對應的點位于虛軸上.

（2）復數(shù)z對應的點位于一、三象限，則2m·（4－m2）＞0m（m－2）（m＋2）＜0m＜－2或0＜m＜2.

∴m＜－2或0＜m＜2時，復數(shù)z對應的點位于一、三象限.

（3）復數(shù)z對應的點位于以原點為圓心，以4為半徑的圓上，則|z|＝＝4m＝0或m＝±2.

∴m＝0或m＝±2時，復數(shù)z對應的點位于以原點為圓心，以4為半徑的圓上.

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