|z|=1,可令z=cost+isint
f(z)=|(1+cost+isint)(cost-isint-i)|=|cost(1+cost)+sint(1+sint)+isintcost-i(1+cost)(1+sint)|
=|1+sint+cost-i(1+sint+cost)|
=|1+sint+cost|*√2
=|1+√2sin(t+π/4)|√2
當(dāng)t=π/4時(shí),即z=(1+i)/√2時(shí),f(z)取最大值√2+2
此時(shí)AZ^2=2+√2
BZ^2=2-√2
AB^2=2
BZ^2+AB^2