已知|z|=1,设μ=z^2-i+1,则|μ|的取值范围是

首先设Z=cosA+isinA,z^2=cos2A+isin2A,带入μ=z^2-i+1得
μ=（cos2A+1）+i(sin2A-1),|μ|=根号下[（cos2A+1）^2+(sin2A-1)^2]
=根号下[3+2(cos2A-sin2A)]<=根号下[3+2根号(2]

因为|z|=1,所以z²=|z|²=1所以μ=2-i
所以|μ|=√5

μ=z^2-i+1，|μ|=|z^2-i+1|,||z^2|-|i+1||<=|μ|<=|z^2|+|-i+1|,（根号2）-1<=|μ|<=（根号2）+1