优优班--学霸训练营 > 知识点挑题
全部资源
          排序:
          最新 浏览

          50条信息

            • 1.

              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.\(-1\)
            • 2.

              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.\(16\) 
            • 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.

              设数列\(\left\{ {{a}_{n}} \right\}\)满足\({{a}_{n}}={{i}^{n}}\),\(i{ }\)是虚数单位,\(n\in {{N}^{*}}\),则数列\(\left\{ {{a}_{n}} \right\}\)的前\(2015\)项和为

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

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

              A.\(\dfrac{2-i}{5}\)
              B.\(\dfrac{2+i}{5}\)
              C.\(\dfrac{1-2i}{5}\)
              D.\(\dfrac{1+2i}{5}\)
            • 6.

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

            • 7.

              已知\(a\)为实数,若复数\(z=({{a}^{2}}-1)+(a+1)i\)为纯虚数,则\(\dfrac{a+{{i}^{2016}}}{1+i}\)的值为\((\)    \()\)     

              A.\(1\)
              B.\(0\)
              C.\(1-i\)
              D.\(1+i\)
            • 8.

              计算\(( \dfrac{1+i}{1-i}{)}^{2017}+ \dfrac{1-i}{1+i}{)}^{2017} =\)(    )

              A.\(-2i\)     
              B.\(0\)      
              C.\(2i\)          
              D.\(2\)
            • 9.

              已知复数\(f(n)={{i}^{n}}(n\in N*)\),则集合\(\left\{ z|z=f(n) \right\}\)中元素的个数是\((\)   \()\)  

              A.\(4\)            
              B.\(3\)          
              C.\(2\)           
              D.\(1\)
            • 10.

              复数 \( \dfrac{2- \sqrt{3i}}{i} \) \((i\)为虚数单位\()\)的虚部是\((\)   \()\)

              A.\(-2\)             
              B.\(2\)          
              C.\(- \sqrt{3} \)
              D.\( \sqrt{3} \)
            0/40

            进入组卷