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            • 1.

              \((1)\)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___________.

            • 2.

              已知\(a\)为实数,若复数\(z=(a^{2}-1)+(a+1)i\)为纯虚数,则\(\dfrac{a+{i}^{2020}}{1+i} =(\)  \()\)

              A.\(1\)                          
              B.\(0\)           
              C.\(1+i\)            
              D.\(1-i\)
            • 3.

              若复数\(z\)满足\(\dfrac{z}{1+i}={{i}^{2015}}+{{i}^{2016}}\) \((i\)为虚数单位\()\),则复数\(z=(\)    \()\)

              A.\(1\)
              B.\(2\)
              C.\(i\)
              D.\(2i\)
            • 4.

              复数\(z=i+{{i}^{2}}+{{i}^{3}}+{{i}^{4}}\)的值是\((\)   \()\)

              A.\(-1\)   
              B.\(0\)
              C.\(1\)   
              D.\(i\)
            • 5.

              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  \((\)    \()\)

              A.\(2\)
              B.\(-2\)
              C.\(2\)或\(-2\)
              D.\(0\)
            • 6.

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

            • 7.

              已知\(i\)为虚数单位,复数\(z=\dfrac{2+i}{1-2i} \),则\(z^{3}=(\)  \()\)

              A.\(i\)                                 
              B.\(-i\)                                
              C.\(1\)                                
              D.\(-1\)
            • 8.

              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\((\)   \()\)

              A.\(i\)
              B.\(-i\)
              C.\(1\)
              D.\(-1\)
            • 9.

              \({{{i}}^{{2018}}}\)的值为\((\)   \()\)

              A.\(1\)
              B.\({i}\)
              C.\(-1\)
              D.\({-i}\)
            • 10.

              已知集合\(M\subseteq \{x|x={{i}^{n}}+{{i}^{-n}},n\in N\}(\)其中\(i\)为虚数单位\()\),则满足条件的集合\(M\)的个数为\((\)  \()\)

              A.\(3\)           
              B.\(4\)       
              C.\(8\)                  
              D.\(16\) 
            0/40

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