设z1=r(cosπ/4+isinπ/4),r>0
z²1=r²(cosπ/2+isinπ/2)=r²i
z²1共轭=-r²i
2/z1=2/r(cosπ/4-isinπ/4)
=√2r-√2i/r
∴z1²共轭-2/z1
=-r²i-√2r+√2i/r
=-√2r+(√2/r-r²)i∈R
∴√2/r-r²=0
∴r³=√2,r=2^(1/6)
∴z1=2^(1/6)(cosπ/4+isinπ/4)
(2)
∵|z1|=2|z2|,
∴|z2|=1/2|z1|=1/2*2^(1/6)=2^(-5/6)
∵ARGz2=ARGz1+π/2=3π/4
∴z2=2^(-5/6)(cos3π/4+isin3π/4)