共50条信息
已知\(a\)为实数，若复数\(z=(a^{2}-1)+(a+1)i\)为纯虚数，则\(\dfrac{a+{i}^{2020}}{1+i} =(\) \()\)
若复数\(z\)满足\(\dfrac{z}{1+i}={{i}^{2015}}+{{i}^{2016}}\) \((i\)为虚数单位\()\)，则复数\(z=(\) \()\)
复数\(z=i+{{i}^{2}}+{{i}^{3}}+{{i}^{4}}\)的值是\((\) \()\)
若\(n\)是大于\(2000\)的奇数，则复数\({{\left( \dfrac{{1}+{i}}{{1}-{i}} \right)}^{2n}}+{{\left( \dfrac{{1}-{i}}{{1}+{i}} \right)}^{2n}}\)的值是 \((\) \()\)
计算：\({{(\dfrac{1+{i}}{\sqrt{2}})}^{2012}}=\) ．
已知复数\(Z=\dfrac{-2+i}{{{i}^{2018}}}(i\)为虚数单位\()\)，则复数\(Z\)的共轭复数\(\overline{Z}\)的虚部为\((\) \()\)
设\(z= \dfrac{1}{2}+ \dfrac{ \sqrt{3}}{2}i(i\)是数单位\()\)，则\(z+2z^{2}+3z^{3}+4z^{4}+5z^{5}+6z^{6}=(\) \()\)
复数\(z{=|}(\sqrt{3}{-}i)i{|+}i^{5}(i\)为虚数单位\()\)，则复数\(z\)的共轭复数为\(({ })\)
计算\({{(\dfrac{\sqrt{2}}{1+i})}^{2006}}\)的值等于______________．
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