优优班--学霸训练营 > 知识点挑题
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            • 1.

              在复平面内,复数\(\dfrac{2-3i}{3+2i}+z\)对应的点的坐标为\((2,-2)\),则\(z\)在复平面内对应的点位于(    )

              A.第一象限
              B.第二象限
              C.第三象限
              D.第四象限
            • 2.

              设\(z\)是虚数,\(ω=z+\dfrac{1}{z}\)是实数,且\(-1 < ω < 2\)

              \((1)\)求\(|z|\)的值及\(z\)的实部的取值范围;

              \((2)\)设\(u=\dfrac{1-z}{1+z} \),求证:\(u\)为纯虚数;

              \((3)\)求\(ω-u^{2}\)的最小值

            • 3.

              若复数\(z=\dfrac{{{i}^{2018}}}{{{(1-i)}^{2}}}(i\)为虚数单位\()\),则\(z\)的共轭复数\(\overline{z}=\)(    )

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

              \(i\)是虚数单位,计算\(\dfrac{1-2{i}}{2+{i}}\) 的结果为       

            • 5. 已知复数\(z= \dfrac {(1-i)^{2}+3(1+i)}{2-i}\).
              \((1)\)求\(z\)的共轭复数\( \overline {z}\);
              \((2)\)若\(az+b=1-i\),求实数\(a\),\(b\)的值.
            • 6.

              已知复数\(w\)满足\(w-1=(1+w)i(i\)为虚数单位\()\),则\(w\)等于(    )

              A.\(1-i\)
              B.\(-i\)
              C.\(-1+i\)
              D.\(i\)
            • 7.

              设复数\(z=1+i(i\)是虚数单位\()\),则\( \dfrac{2}{z}+z^{2}=(\)  \()\)

              A.\(1+i\)                                                      
              B.\(2-i\)

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

              已知复数\(z\)在复平面内对应点是\((1,-2)\),\(i\)为虚数单位,则\( \dfrac{z+2}{z-1} =(\)   \()\)

              A.\(-1-i\)   
              B.\(1+i\)   
              C.\(1- \dfrac{3}{2}i \)
              D.\(1+ \dfrac{3}{2}i \)
            • 9.

              复数\( \dfrac{2}{1+i} \)的虚部是\((\)   \()\)

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

              设\(z\)是虚数,\(w=z+ \dfrac{1}{z} \)是实数,且\(-1 < w < 2\)

              \((1)\)求\(\left|z\right| \)的值及\(z\)的实部的取值范围.

              \((2)\)设\(μ= \dfrac{1-z}{1+z} \),求\(w-{μ}^{2} \)的最小值.

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