共50条信息
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 ．
计算\((1)\dfrac{2+2i}{1-i}+{{\left( \dfrac{\sqrt{2}}{1+i} \right)}^{2016}}\) \((2)\)计算 \(\int_{-2}^{0}{\sqrt{4-{{x}^{2}}}}dx\)
设复数\(x= \dfrac{2i}{1-i}(i\)是虚数单位\()\)，则\(C\rlap{^{1}}{_{2 015}}x+C\rlap{^{2}}{_{2 015}}x^{2}+C\rlap{^{3}}{_{2 015}}x^{3}+…+C\rlap{_{2 015}}{^{2 015}}x^{2\;015}=\)____________．
若复数\(z= \dfrac{1+i}{1-i} \)，\( \overset{-}{z} \)为\(z \)的共轭复数，则\(( \overset{-}{z}{)}^{2017} =\)_________________．
\((1) \dfrac{2+2i}{{\left(1-i\right)}^{2}} +( \dfrac{ \sqrt{2}}{1+i} )^{2010}\)；
\((2)\)已知复数\(z\)的共轭复数为\( \overset{¯}{z} \)，且\(z\)\(· \overset{¯}{z} -3i\)\(z\)\(= \dfrac{10}{1-3i} \)，求\(z\)．
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