共50条信息
设\(i\)为虚数单位，复数\(z\)满足\(z(1+i)=2{{i}^{2018}}\)，则\(z\)等于
已知复数\(Z{=}i+2{{i}^{2}}+{{i}^{10}}\)，则\(|z|=\)( )
在复平面内，复数\(z\)满足\(z\left( 1+{{i}^{5}} \right)=\left| 1-\sqrt{3}i \right|\)，则\(z\)的共轭复数对应的点位于\((\) \()\)
\((1)\)计算\({{\left[ (1+2i)\cdot {{i}^{100}}+{{(\dfrac{1-i}{1+i})}^{5}} \right]}^{2}}-{{(\dfrac{1+i}{\sqrt{2}})}^{20}}\)
\((2)\)已知\(z\)，\(ω \)为复数，\((1+3i)·z\)为纯虚数，\(ω= \dfrac{z}{2+i} \)，且\(|ω|=5 \sqrt{2} \)，求复数\(z\)．
若\(z=\left(a- \sqrt{2}\right)+ai \)为纯虚数，其中\(a∈R \)，则\( \dfrac{a+{i}^{7}}{1+ai}= (\) \()\)
已知复数\(zi={{\left( \dfrac{i+1}{i-1} \right)}^{2018}}(i\)为虚数单位\()\)，则\(z\)的虚部( )
已知\(i\)为虚数单位，复数\(z\)满足\(z(1−i)=1+i \)，则\({z}^{2017}= \)( )
已知\(a\)为实数，若复数\(z=({{a}^{2}}-1)+(a+1)i\)为纯虚数，则\(\dfrac{a+{{i}^{2016}}}{1+i}\)的值为\((\) \()\)
\(i+{i}^{2}+{i}^{3}+...+{i}^{2017} (\) \()\)
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