1-根号3i/(根号3+i)的平方等于平方是根号3+i的平方,不是整体的平方
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![1-根号3i/(根号3+i)的平方等于平方是根号3+i的平方,不是整体的平方](/uploads/image/z/2554617-57-7.jpg?t=1-%E6%A0%B9%E5%8F%B73i%2F%28%E6%A0%B9%E5%8F%B73%2Bi%29%E7%9A%84%E5%B9%B3%E6%96%B9%E7%AD%89%E4%BA%8E%E5%B9%B3%E6%96%B9%E6%98%AF%E6%A0%B9%E5%8F%B73%2Bi%E7%9A%84%E5%B9%B3%E6%96%B9%EF%BC%8C%E4%B8%8D%E6%98%AF%E6%95%B4%E4%BD%93%E7%9A%84%E5%B9%B3%E6%96%B9)
1-根号3i/(根号3+i)的平方等于平方是根号3+i的平方,不是整体的平方
1-根号3i/(根号3+i)的平方等于
平方是根号3+i的平方,不是整体的平方
1-根号3i/(根号3+i)的平方等于平方是根号3+i的平方,不是整体的平方
原式=(1-√3i)/(√3+i)^2
=(1-√3i)/(2+2√3i)
=(1-√3i)^2/[2*(1-3)]
=(-2-2√3i)/(-4)
=(1+√3i)/2.
若前面没有括号,
原式=1-√3i/(√3+i)^2
=(7+√3i)/4.
也差不多,用两种方法:
(1-根号3i)/(根号3+i)^2
=(1-根号3i)/[i(1-根号3i)(根号3+i)]
=1/[i(根号3+i)]
=1/(-1+根号3·i)
=(-1-根号3·i)/[(-1+根号3·i)·(-1-根号3·i)]
=(-1-根号3·i)/4
或用三角函数:
(1-根号3i)/(根号3+i)^2
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也差不多,用两种方法:
(1-根号3i)/(根号3+i)^2
=(1-根号3i)/[i(1-根号3i)(根号3+i)]
=1/[i(根号3+i)]
=1/(-1+根号3·i)
=(-1-根号3·i)/[(-1+根号3·i)·(-1-根号3·i)]
=(-1-根号3·i)/4
或用三角函数:
(1-根号3i)/(根号3+i)^2
=2(1/2-根号3/2·i)/[2(根号3/2+1/2·i)]^2
=2[cos(-π/3)+isin(-π/3)]/[4·(cosπ/6+isinπ/6)^2]
=1/2·[cos(-π/3)+isin(-π/3)]/(cosπ/3+isinπ/3)
=1/2·[cos(-π/3-π/3)+isin(-π/3-π/3)]
=1/2·[cos(-2π/3)+isin(-2π/3)]
=1/2·[-1/2+i·(-根号3/2)]
=-1/4-根号3/4·i
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