优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知\(a\in R\),若\(\dfrac{a+2i}{4-i}\)是纯虚数,则在复平面内,复数\(z=ai+{{i}^{2018}}\)所对应的点位于\((\)    \()\)

              A.第一象限   
              B.第二象限   
              C.第三象限   
              D.第四象限
            • 2. 已知\(i\)是虚数单位,则\((2+i)(3+i)=(\)  \()\).
              A.\(5-5i\)
              B.\(7-5i\)
              C.\(5+5i\)
              D.\(7+5i\)
            • 3.

              设\(i\)为虚数单位,则\((\dfrac{1{+}i}{i})^{2014}\)等于\(({  })\)

              A.\(2^{1007}i\)
              B.\({-}2^{1007}i\)
              C.\(2^{2014}\)
              D.\({-}2^{2014}\)
            • 4.

              已知\(i\)是虚数单位,复数\(z=(1+i)·i^{3}\),则 \(\dfrac{1}{z}\) 的共轭复数是(    )

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

               \(f\left(n\right)={i}^{n}+{i}^{-n}\left(n∈N\right) \) ,则集合\(\left\{x \left|x=f\left(n\right) \right.\right\} \)中元素的个数为

              A.\(1\)            
              B.\(2\)        
              C.\(3\)            
              D.无穷多个
            • 7.

              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.\(1\)
            • 8.

              已知\(i\)是虚数单位,则\(1+\)\(i\)\(+\)\(i\)\({\,\!}^{2}…+\)\(i\)\({\,\!}^{2018}\)等于(    )

              A.\(1-\) \(i\)
              B.\(1+\) \(i\)
              C.\(-\) \(i\)
              D.\(i\)
            • 9. 已知i是虚数单位,则1+i+i2…+i100等于(  )
              A.1-i
              B.1+i
              D.1
            • 10. (1+i)20-(1-i)20的值为(  )
              B.1024
              C.-1024
              D.-10241
            0/40

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