设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围.要有具体过程·注明:a代表的是角度
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![设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围.要有具体过程·注明:a代表的是角度](/uploads/image/z/3582283-67-3.jpg?t=%E8%AE%BE%E5%A4%8D%E6%95%B0z%E6%BB%A1%E8%B6%B34z%2B2%2Az%E7%9A%84%E5%85%B1%E8%BD%AD%E5%A4%8D%E6%95%B0%3D3%E5%80%8D%E6%A0%B9%E5%8F%B73%2Bi%2Cw%3Dsina-icosa%2C%E6%B1%82z%E7%9A%84%E5%80%BC%E5%92%8C%7Cz-w%7C%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.%E8%A6%81%E6%9C%89%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B%C2%B7%E6%B3%A8%E6%98%8E%EF%BC%9Aa%E4%BB%A3%E8%A1%A8%E7%9A%84%E6%98%AF%E8%A7%92%E5%BA%A6)
设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围.要有具体过程·注明:a代表的是角度
设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围.
要有具体过程·注明:a代表的是角度
设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围.要有具体过程·注明:a代表的是角度
z=c+bi,
4(c+bi)+2(c-bi) = 6c+2bi=3*3^(1/2)+i,
c=3^(1/2)/2,b=1/2.
z = 3^(1/2)/2 + i/2.
z-w=3^(1/2)/2 + i/2 -sina+icosa = [3^(1/2)/2 -sina] + i[1/2 + cosa]
|z-w|^2 = [3^(1/2)/2 - sina]^2 + [1/2 + cosa]^2
= 3/4 -3^(1/2)sina + 1/4 + cosa + 1
= 2 + 2[cosa*1/2-sina*3^(1/2)/2]
= 2 + 2cos[a+PI/3]
0 <= |z-w|^2 = 2 + 2cos[a+PI/3] <= 4,
0 <= |z-w| <= 2.
设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围。
要有具体过程·注明:a代表的是角度
z=c+bi,
4(c+bi)+2(c-bi) = 6c+2bi=3*3^(1/2)+i,
c=3^(1/2)/2,b=1/2.
z = 3^(1/2)/2 + i/2.
z-w=3^(1/2)...
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设复数z满足4z+2*z的共轭复数=3倍根号3+i,w=sina-icosa,求z的值和|z-w|的取值范围。
要有具体过程·注明:a代表的是角度
z=c+bi,
4(c+bi)+2(c-bi) = 6c+2bi=3*3^(1/2)+i,
c=3^(1/2)/2,b=1/2.
z = 3^(1/2)/2 + i/2.
z-w=3^(1/2)/2 + i/2 -sina+icosa = [3^(1/2)/2 -sina] + i[1/2 + cosa]
|z-w|^2 = [3^(1/2)/2 - sina]^2 + [1/2 + cosa]^2
= 3/4 -3^(1/2)sina + 1/4 + cosa + 1
= 2 + 2[cosa*1/2-sina*3^(1/2)/2]
= 2 + 2cos[a+PI/3]
0 <= |z-w|^2 = 2 + 2cos[a+PI/3] <= 4,
0 <= |z-w| <= 2.
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