问题描述：
若z∈C,|z|=2,复数w=z^2-3+4i,则|w|的取值范围
问题解答：
我来补答
|z|=2
设z=2cosx+2sinx*i.x∈R
w=（2cosx+2sinx*i）^2-3+4i
=4*（cosx+sinx*i）^2-3+4i
=4*（cos^2x-sin^2x+2sinxcosx*i）-3+4i
=4*（cos2x+sin2x*i）-3+4i
=4cos2x+4sin2x*i-3+4i
=4cos2x-3+4sin2x*i+4i
=4cos2x-3+（sin2x+1）*4i
|w|^2=（4cos2x-3）^2+16*（sin2x+1）^2
=16cos^2（2x）+9-24cos2x+16*[sin^2（2x）+1+2sin2x]
=16cos^2（2x）+9-24cos2x+16sin^2（2x）+16+32sin2x
=16cos^2（2x）+16sin^2（2x）
+32sin2x-24cos2x+9+16
=16+32sin2x-24cos2x+25
=32sin2x-24cos2x+41
=40sin(2x+φ)+41 (φ∈R)
sin(2x+φ)∈[-1,1]
|w|^2∈[1,81]
|w|∈[1,9]
|w|的取值范围是[1,9]
