优优班--学霸训练营 > 知识点挑题
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            • 1.

              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                         

            • 2.

              \(\left( \left. \dfrac{1+i}{1-i} \right. \right)^{2 018} =\)________.

            • 3.

              复数\({{\left( \dfrac{1-i}{1+i} \right)}^{10}}\)的值是____________.

            • 4.

              \(\left( \left. \dfrac{1+i}{1-i} \right. \right)^{6} + \dfrac{ \sqrt{2}+ \sqrt{3}i}{ \sqrt{3}- \sqrt{2}i}=\)_______.

            • 5.

              复数\(z=a(1+i)-2(i\)为虚数单位\()\)为纯虚数,则\(a=\)________;\(|z|=3\)表示的图形是_______________________.

            • 6.

              \((1)\)一同学在电脑中打出如下若干个圆\((\)图中\(●\)表示实圆,\(○\)表示空心圆\()\):\(●○●●○●●●○●●●●○●●●●●○●●●●●●○\),若将此若干个圆依次复制得到一系列圆,那么在前\(2018\)个圆中,有_______个空心圆.

              \((2)\)设\({{Z}_{1}}= i^{4} + i^{5}+ i^{6}+…+ i^{12}\),\(Z{}_{2}= i^{4} · i^{5}·i^{6}·…· i^{12}\),则\(Z_{1}\) ,\(Z{}_{2}\)关系为________________

              \((3)y=f\left(x\right) \)在\(x={x}_{0} \)处可导,且\( \lim\limits_{∆x→0} \dfrac{f\left({x}_{0}-3∆x\right)-f\left({x}_{0}\right)}{∆x}=1 \),则\(f{{'}}\left({x}_{0}\right) =\)                 \(\_\) 

              \((4)\)若函数\(f(x)={{x}^{3}}-a{{x}^{2}}+4\)在\((0,2)\)内单调递减,则实数\(a\)的取值范围是___________.

            • 7.

              计算:\({{(\dfrac{1+{i}}{\sqrt{2}})}^{2012}}=\)     

            • 8.

              计算\(\left(2+{i}^{15}\right)-{\left( \dfrac{1+i}{ \sqrt{2}}\right)}^{22} =\)___________.

            • 9.

              已知\(i\)是虚数单位,则\(\left(\begin{matrix} \begin{matrix} \dfrac{ \sqrt{2}}{1-i} \end{matrix}\end{matrix}\right)^{2 016} +\left(\begin{matrix} \begin{matrix} \dfrac{1+i}{1-i} \end{matrix}\end{matrix}\right)^{6} =\)________.

            • 10.

              计算\(i+2{{i}^{2}}+3{{i}^{3}}+4{{i}^{4}}+...+20{{i}^{20}}=\_\_\_\_\_\)

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