已知α属于(0,π),求复数z=1-cosα+isinα的模及辐角主值
问题描述:
已知α属于(0,π),求复数z=1-cosα+isinα的模及辐角主值
答
z=1-cos a+isin a = 2sin^2(a/2) + i(2sin(a/2)cos(a/2)) = 2sin(a/2) * (sin(a/2) + icos(a/2))= 2sin(a/2) * (cos(π/2 - a/2) + isin(π/2 - a/2))模为2sin(a/2) 辐角为(π/2 - a/2)度