设z属于C,满足z+1/z属于R,z-(1/4)是纯虚数,求z
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![设z属于C,满足z+1/z属于R,z-(1/4)是纯虚数,求z](/uploads/image/z/8785397-29-7.jpg?t=%E8%AE%BEz%E5%B1%9E%E4%BA%8EC%2C%E6%BB%A1%E8%B6%B3z%2B1%2Fz%E5%B1%9E%E4%BA%8ER%2Cz-%281%2F4%29%E6%98%AF%E7%BA%AF%E8%99%9A%E6%95%B0%2C%E6%B1%82z)
设z属于C,满足z+1/z属于R,z-(1/4)是纯虚数,求z
设z属于C,满足z+1/z属于R,z-(1/4)是纯虚数,求z
设z属于C,满足z+1/z属于R,z-(1/4)是纯虚数,求z
设z=a+bi,z-(1/4)是纯虚数可得 a+bi-1/4=(a-1/4)+bi是纯虚数,a-1/4=0,a=1/4.
z+1/z属于R,可列:a+bi+[1/(a+bi)],后一项上下同乘(a-bi)得:
a+bi+(a-bi)/(a^2-b^2),因为它属于R实数,所以虚部为0即:
解不下去了.你表达式哪写错了?