f(z)=z^4+4z^3+8z^2+8z+5
=z^2(z+2)^2+4(z+1)^2+1
z=-1+2i代入得:
f(-1+2i)=(-1+2i)^2(1+2i)^2+4(2i)^2+1
=(4i^2-1)^2+16i^2+1
=25-16+1
=10
f(z)=z^4+4z^3+8z^2+8z+5
=z^2(z+2)^2+4(z+1)^2+1
z=-1+2i代入得:
f(-1+2i)=(-1+2i)^2(1+2i)^2+4(2i)^2+1
=(4i^2-1)^2+16i^2+1
=25-16+1
=10