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设A、B、C分别为复数平面上代表1+i、1+iZ,以及1-i的点.请问下...

设A、B、C分别为复数平面上代表1+i、1+iZ,以及1-i的点.请问下列哪些选项所对应的点落在△OAB的内部?
(1)cos60°
(2)cos50°+isin50°
(3)manfen5.com 满分网
(4)manfen5.com 满分网
(5)(cos30°+isin30°)25
根据所给的三个复数的代数形式,写出复数对应的点,得到以这三个点为顶点的三角形,把所给的五个条件进行验证,从模长到幅角两个方面来说明. 【解析】 可知与均与x轴夹45度角. 且, (1),故cos60°位于x轴上 距离原点单位之处,所以cos60°位 于△ABC内部. (2)cos50°+isin50°与原点距离为,且与x轴夹50度角的点, 故此点在△ABC外部.(因为50°>45°) (3)在复数平面对应到点∵在上, ∴在△ABC内部. (4)在复数平面对应到点∵在上, ∴在外部. (5)(cos30°+isin30°)25=cos750°+isin750°=cos30°+isin30°, 此点与原点距离为,且与x轴夹30度角的点, 故此点在△ABC内部.(因为30°<45°) 答:(1)(3)(5)
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