f(z)=2z+z的共轭-3i,f(z的共轭+i)=6-3i,试求f(-z)

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f(z)=2z+z的共轭-3i,f(z的共轭+i)=6-3i,试求f(-z)

f(z)=2z+z的共轭-3i,f(z的共轭+i)=6-3i,试求f(-z)
f(z)=2z+z的共轭-3i,f(z的共轭+i)=6-3i,试求f(-z)

f(z)=2z+z的共轭-3i,f(z的共轭+i)=6-3i,试求f(-z)
令 z=a+bi,(a,b∈R),则
f(z)=2(a+bi)+(a-bi)-3i=3a+(b-3)i
f(z的共轭+i)=f[a+(1-b)i]
=3a+(-b-2)i
=6-3i
∴ 3a=6,-b-2=-3
解得,a=2,b=1
∴ f(-z)=f(-2-i)=-6-4i
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