已知复数z满足(1+根号3i)z=1+i,其中I为虚数单位,则绝对值z=

方法一：z(1+√3i)=1+i所以z=(1+i)/(1+√3i)=(1+i)(1-√3i)/[(1+√3i)(1-√3i)]=[(1+√3)+(1-√3)i]/4|z|=√[(1+√3)²+(1-√3)²]/4=2√2/4=√2/2.方法二：因为z=(1+i)/(1+√3i),所以|z|=|(1+i)/(1+√3i)|=...