共50条信息
\((1)\dfrac{{2}+{2i}}{{{({1}-{i})}^{{2}}}}+{{\left( \dfrac{\sqrt{{2}}}{{1}+{i}} \right)}^{{2016}}}\)；
\((2)i+i^{2}+…+i^{2017}\)．
\(\left( \left. \dfrac{1+i}{1-i} \right. \right)^{2 018} =\)________．
已知\(z=\dfrac{1+i}{\sqrt{2}}\)，则\(1+z^{50}+z^{100}\)的值是\((\) \()\)
\((1)\dfrac{{2}+{2i}}{{{({1}-{i})}^{{2}}}}+{{\left( \dfrac{\sqrt{{2}}}{{1}+{i}} \right)}^{{2010}}}\)；
\((2)(4-i^{5})(6+2i^{7})+(7+i^{11})(4-3i)\)．
复数\({{\left( \dfrac{1-i}{1+i} \right)}^{10}}\)的值是____________．
复数\(z{=|}(\sqrt{3}{-}i)i{|+}i^{2017}(i\)为虚数单位\()\)，则复数\(z\)的共轭复数为\(({ })\)
计算\(\left(2+{i}^{15}\right)-{\left( \dfrac{1+i}{ \sqrt{2}}\right)}^{22} =\)___________．
设复数\({{z}_{1}}=\dfrac{\sqrt{3}}{2}+\dfrac{1}{2}i\)，\({{z}_{2}}=3+4i\)，其中\(i\)为虚数单位，则\(\dfrac{|z_{1}^{2016}|}{|{{z}_{2}}|}=(\) \()\)
已知\(i\)是虚数单位，则\(\left(\begin{matrix} \begin{matrix} \dfrac{ \sqrt{2}}{1-i} \end{matrix}\end{matrix}\right)^{2 016} +\left(\begin{matrix} \begin{matrix} \dfrac{1+i}{1-i} \end{matrix}\end{matrix}\right)^{6} =\)________．
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