优优班--学霸训练营 > 知识点挑题
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            • 1. 复数\( \dfrac{i^{2}+i^{3}+i^{4}}{1-i}=(\)  \()\)
              A.\(- \dfrac{1}{2}\)\(-\)\( \dfrac{1}{2}\)\(i\)     
              B.\(- \dfrac{1}{2}\)\(+\)\( \dfrac{1}{2}\)\(i\)       
              C.\( \dfrac{1}{2}\)\(-\)\( \dfrac{1}{2}\)\(i\)   
              D.\( \dfrac{1}{2}\)\(+\)\( \dfrac{1}{2}\)\(i\)
            • 2.

              复数\((\dfrac{1{+}i}{1{-}i})^{100}\)的值等于\(({  })\)

              A.\(1\)                                
              B.\({-}1\)
              C.\(i\)
              D.\({-}i\)
            • 3.

              设复数\(x{=}\dfrac{2i}{1{-}i}(i\)是虚数单位\()\),则\(C{{ }}_{2016}^{1}x{+}C{{ }}_{2016}^{2}x^{2}{+}C{{ }}_{2016}^{3}x^{3}{+…+}C{{ }}_{2016}^{2016}x^{2016}{=}({  })\)

              A.\(0\)              
              B.\({-}2\)
              C.\({-}1{+}i\)
              D.\({-}1{-}i\)
            • 4.

              已知\(i\)为虚数单位,则复数\({{\left( \dfrac{1-i}{1+i} \right)}^{2018}}=\) 

              A.\(-1\)
              B.\(1\)
              C.\(-i\)
              D.\(i\)
            • 5. \((1)\)\(i\)是虚数单位,\(( \dfrac{ \sqrt{2}}{1-i} \)\()\)\(2 018\)\(+\)\(( \dfrac{1+i}{1-i} \)\()\)\(6\)\(=\)________.
              \((2)\)若\(f(x)=x\)\(3\)\(+ax\)\(2\)\(+bx+a\)\(2\)在\(x=1\)处有极值\(10\),则\(a+b=\)________.

              \((3).\)曲线\(f(x)=\ln x- \dfrac{2^{x}}{\ln 2}\)在\(x=1\)处的切线方程为                   

              \((4)\)已知\(f{{{'}}}\left( x \right)\)是函数\(f\left( x \right)\)的导函数,且对任意的实数\(x\)都有\(f{{{'}}}\left( x \right)={{e}^{x}}\left( 2x+3 \right)+f\left( x \right)(e\)是自然对数的底数\()\),\(f\left( 0 \right)=1\),若不等式\(f\left( x \right)-k < 0\)的解集中恰有两个整数,则实数\(k\)的取值范围是______

            • 6.

              \(i^{2}+ i^{4}=\)                           

            • 7.

              在复平面内,复数\(z= \dfrac{2}{3-i}+{i}^{3} \)对应的点位于\((\)  \()\)

              A.第一象限        
              B.第二象限       
              C.第三象限       
              D.第四象限
            • 8.

              若复数\(z=(a-1)i+(a^{2}-1)i^{4}(a∈R)\)是纯虚数,则\(a\)等于

              A.\(1\)
              B.\(0\)
              C.\(-1\)
              D.\(±1\)
            • 9.

              复数\(z\)\(=i+i^{2}+i^{3}+i^{4}+……+i^{12}\)的值是                

            • 10.

              \(i\) 为虚数单位,\({{i}^{607}}=(\)   \()\)

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