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            • 1.

              下列命题中,错误命题的序号是____________.

              \(①\)两个复数不能比较大小;\(②z_{1}\),\(z_{2}\),\(z_{3}∈C\),若\((z_{1}-z_{2})^{2}+(z_{2}-z_{3})^{2}=0\),则\(z_{1}=z_{3}\);

              \(③\)若\((x^{2}-1)+(x^{2}+3x+2)i\)是纯虚数,则实数\(x=±1\);\(④z\)是虚数的一个充要条件是\(z+\overset{\_}{{z}}\,∈R\).

            • 2.

              若复数\(z\)满足\((3-4i)z=\left| 4+3i \right|\),则\(z\)的虚部为________

            • 3.

              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                         

            • 4.

              \((1)\)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___________.

            • 5.

              \((1)\)设集合\(A=\{x|x^{4}-1=0,x∈C\}\),\(z=2-3i\),若\(x∈A\),则\(|x-z|\)最大值是________.

              \((2)\)根据如图所示的流程图,回答下面问题:若\(a=5^{0.6}\),\(b=0.6^{5}\),\(c=\log _{0.6}5\),则输出的数是________.

              \((3)\)已知球\(0\)的直径长为\(12\),当它的内接正四棱锥的体积最大时,则该四棱锥的高为________.

              \((4)\)对于三次函数\(f(x)=ax^{3}+bx^{2}+cx+d(a\neq 0)\)给出定义:设\(f′(x)\)是函数\(y=f(x)\)的导数,\(f″(x)\)是函数\(f′(x)\)的导数,若方程\(f″(x)=0\)有实数解\(x_{0}\),则称点\((x_{0},f(x_{0}))\)为函数\(y=f(x)\)的“拐点”,某同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且“拐点”就是对称中心。给定函数\(f(x)=\dfrac{1}{3}{{x}^{3}}-\dfrac{1}{2}{{x}^{2}}+3x-\dfrac{5}{12}\),请你根据上面探究结果,计算\(f( \dfrac{1}{2017})+f( \dfrac{2}{2017})+f( \dfrac{3}{2017})+⋯+f( \dfrac{2016}{2017})= \)                             

            • 6.

              设复数\(x= \dfrac{2i}{1-i}(i\)是虚数单位\()\),则\(C\rlap{^{1}}{_{2 015}}x+C\rlap{^{2}}{_{2 015}}x^{2}+C\rlap{^{3}}{_{2 015}}x^{3}+…+C\rlap{_{2 015}}{^{2 015}}x^{2\;015}=\)____________.

            • 7.
              复数\(z=(m^{2}-m-4)+(m^{2}-5m-6)i(m∈R)\),如果\(z\)是纯虚数,那么\(m=\) ______ .
            • 8.

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

            • 9. 已知i1=i,i2=-1,i3=-i,i4=1,i5=i,由此可猜想i2016= ______
            • 10.

              \(i\)是虚数单位,复数\(z\)满足\((1+i)z=2\),则\(z\)的实部为___              __.

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