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复数Z=a+bi(a>0,b>0) |Z|=1,且|z-1/2|=根号3/2 求z

学习时间:2026-04-04 19:59:21 阅读：7647

复数Z=a+bi(a>0,b>0) |Z|=1,且|z-1/2|=根号3/2 求z

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高挑的奇异果

2026-04-04 19:59:21

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z=a+bi|z|=1a^2+b^2 =1 (1)|z-1/2| =√3/2(a-1/2)^2 +b^2 = 3/4 (2)(1)-(2)a-1/4 = 1/4a= 1/2b= √3/2 or -√3/2z = 1/2 +(√3/2) i or 1/2 -(√3/2) i

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2026-04-04 19:59:21
z=a+bi|z|=1a^2+b^2 =1 (1)|z-1/2| =√3/2(a-1/2)^2 +b^2 = 3/4 (2)(1)-(2)a-1/4 = 1/4a= 1/2b= √3/2 or -√3/2z = 1/2 +(√3/2) i or 1/2 -(√3/2) i

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