设z是复数且满足|z|^2+zi-z把i≤0,则Rez+imz的取值范围?

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设z是复数且满足|z|^2+zi-z把i≤0,则Rez+imz的取值范围?设z是复数且满足|z|^2+zi-z把i≤0,则Rez+imz的取值范围?设z是复数且满足|z|^2+zi-z把i≤0,则Re

设z是复数且满足|z|^2+zi-z把i≤0,则Rez+imz的取值范围?
设z是复数且满足|z|^2+zi-z把i≤0,则Rez+imz的取值范围?

设z是复数且满足|z|^2+zi-z把i≤0,则Rez+imz的取值范围?
设z=x+yi.gz=x-yi.(x,y∈R),则|z|²+zi-gzi≤0.x²+y²-2y≤0.===>x²+(y-1)²≤1.可设x=rcost,y=1+rsint.(t,r∈R,且0≤r≤1).===>x+y=(√2)rsin[t+(π/4)]+1.===>1-√2≤x+y≤1+√2.

设z=a+bi,则a^2+b^2+ia-b-a-bi《0,所以a^2+b^2-b-a《0,且a-b=0,所以2a^2-2a《0,0《a《1,同理,0《b《1,Rez+imz=a+b,则0《Rez+imz《2