数学一道复数题已知|z|=1,设M=z的平方-i+1,则|M|的取值范围

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|z|=1令z=cosθ+isinθ
M=cos²θ+2isinθcosθ-sin²θ-i+1
=cos2θ+isin2θ-i+1
=(cos2θ+1)+(sin2θ-1)i
|M|²=(cos2θ+1)²+(sin2θ-1)²
=cos²2θ+sin²2θ-2sin2θ+2cos2θ+2
=-2(sin2θ-cos2θ)+3
=-2√2sin(2θ-π/4)+3
-1