1+cosα+isinα=2[cos(a/2)]^2+i*2sin(a/2)cos(a/2)=2cos(a/2)[cos(a/2)+isin(a/2)],|1+cosα+isinα|=2cos(a/2)[cos(a/2)+isin(a/2)]=|2cos(a/2)|*|cos(a/2)+isin(a/2)|=2cos(a/2).