优优班--学霸训练营 > 知识点挑题
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            • 1.

              设复数\(x=\dfrac{2i}{1-i}(i\)是虚数单位\()\),则\(C_{2018}^{1}x+C_{2018}^{2}{x}^{2}+C_{2018}^{3}{x}^{3}+…+C_{2018}^{2018}{x}^{2018}= \)

              A.\(-2\)
              B.\(0\)
              C.\(-1+i\)
              D.\(-1-i\)
            • 2.

              \(i\)为虚数单位,则\({{(\dfrac{1+i}{1-i})}^{2018}}=\)_______

            • 3.

              \((1)\)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\(f( \dfrac{1}{2017})+f( \dfrac{2}{2017})+f( \dfrac{3}{2017})+⋯+f( \dfrac{2016}{2017})= \)                             

            • 4.

              设\(z= \dfrac{1}{2}+ \dfrac{ \sqrt{3}}{2}i(i\)是数单位\()\),则\(z+2z^{2}+3z^{3}+4z^{4}+5z^{5}+6z^{6}=(\)   \()\)


              A.\(6z\)            
              B.\(6z^{2\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\)
              C.\(6\overline{z}\)
              D.\(-6z\)
            • 5.

              计算\((4-{{i}^{5}})(6+2{{i}^{7}})+(7+{{i}^{11}})(4-3i)\)    

            • 6.

              已知\(1+x+x^{2}=0\),求:

              \((1)1+x+x^{2}+…+x^{100}\);

              \((2)x^{2001}+x^{2002}+…+x^{2007}\).

            • 7. 已知复数\(z=\dfrac{i+{i}^{2}+{i}^{3}+⋯+{i}^{2018}}{1+i} \),则复数\(z\)在复平面内对应点的坐标为________.
            • 8.

              复数\(x < 0\)等于   \((\)      \()\)

              A.\(x < 0\)
              B.\(x < 0\)
              C.\(x < 0\)
              D.\(x < 0\)
            • 9.

              设\(i\)为虚数单位,复数\(z\)满足\(z(1+i)=2{{i}^{2018}}\),则\(z\)等于

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

              计算\((1)\dfrac{2+2i}{1-i}+{{\left( \dfrac{\sqrt{2}}{1+i} \right)}^{2016}}\)      \((2)\)计算  \(\int_{-2}^{0}{\sqrt{4-{{x}^{2}}}}dx\)   

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