共50条信息
已知\(i\)是虚数单位，则\({{\left( \dfrac{1-i}{1+i} \right)}^{6}}+{{\left( \dfrac{\sqrt{2}}{1-i} \right)}^{2018}}=\)____________________\(.\)
\( \dfrac{-2 \sqrt{3}+i}{1+2 \sqrt{3}i}+\left( \left. \dfrac{ \sqrt{2}}{1-i} \right. \right)^{2 017} =\)________．
已知复数\(z=i+i^{2}+i^{3}+…+i^{2019}\)，则\(z=\)________．
\((1)\dfrac{{2}+{2i}}{{{({1}-{i})}^{{2}}}}+{{\left( \dfrac{\sqrt{{2}}}{{1}+{i}} \right)}^{{2016}}}\)；
\((2)i+i^{2}+…+i^{2017}\)．
设\(f(n)={\left( \dfrac{1+i}{1-i}\right)}^{n}+{\left( \dfrac{1-i}{1+i}\right)}^{n}\left(n∈N\right) \)，则集合\(\left\{x \left|x=f(n) \right.\right\} \)的子集个数是 ．
\(\left( \left. \dfrac{1+i}{1-i} \right. \right)^{2 018} =\)________．
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____________．
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