共50条信息
在复平面内,复数\(\dfrac{2-3i}{3+2i}+z\)对应的点的坐标为\((2,-2)\),则\(z\)在复平面内对应的点位于( )
设\(z\)是虚数,\(ω=z+\dfrac{1}{z}\)是实数,且\(-1 < ω < 2\)
\((1)\)求\(|z|\)的值及\(z\)的实部的取值范围;
\((2)\)设\(u=\dfrac{1-z}{1+z} \),求证:\(u\)为纯虚数;
\((3)\)求\(ω-u^{2}\)的最小值
若复数\(z=\dfrac{{{i}^{2018}}}{{{(1-i)}^{2}}}(i\)为虚数单位\()\),则\(z\)的共轭复数\(\overline{z}=\)( )
复数\(\dfrac{5i}{1{+}2i}\)的虚部是\(({ })\)
已知\(i\)为虚数单位,且\( \dfrac{2+i}{1+2i}=x+yi\left(x,y∈R\right),则\left|x+yi\right|= \)
\(i\)是虚数单位,计算\(\dfrac{1-2{i}}{2+{i}}\) 的结果为
已知复数\(w\)满足\(w-1=(1+w)i(i\)为虚数单位\()\),则\(w\)等于( )
设复数\(z=1+i(i\)是虚数单位\()\),则\( \dfrac{2}{z}+z^{2}=(\) \()\)
记复数\(z=a+bi(i\)为虚数单位\()\)的共轭复数为\(\overline{z}=a-bi(a,b∈R)\),已知\(z=2+i\),那么\(\overline{z^{2}}=\) \(.\)
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