优优班--学霸训练营 > 知识点挑题
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            • 1. 已知复数\(z\)满足\( \dfrac {z+2}{z-2}=i(\)其中\(i\)是虚数单位\()\),则\(|z|=\) ______ .
            • 2.

              设\(z_{1}\),\(z_{2}\)是复数,则下列命题中的假命题是\((\)  \()\)

              A.若\(|z_{1}-z_{2}|=0\),则\(\overline{z}_{1}=\overline{z}_{2}\)
              B.若\(z_{1}=\overline{z}_{2}\),则\(\overline{z}_{1}=z_{2}\)

              C.若\(|z_{1}|=|z_{2}|\),则\(z_{1}·\overline{z}_{1}=z_{2}·\overline{z}_{2}\)
              D.若\(|z_{1}|=|z_{2}|\),则\(z\rlap{_{1}}{^{2}}=z\rlap{_{2}}{^{2}}\)
            • 3.
              已知复数\(z=1+i\),则下列命题中正确的个数是(    )

              \(①|z|=\)\( \sqrt{2}\);\(②z=1-i\);\(③z\)的虚部为\(i\);\(④z\)在复平面内对应的点位于第一象限.

              A.\(1\)                                                             
              B.\(2\)

              C.\(3\)                                                             
              D.\(4\)
            • 4.

              设复数\(z\)\(=-1-i(i\)为虚数单位\()\),\(z\)的共轭复数为\(\overline{z}\),则\(|(1-\)\(z\)\()·\overline{z}|=\)

              A.\( \sqrt{10}\)        
              B.\(2\)        
              C.\( \sqrt{2}\)        
              D.\(1\)
            • 5. 设复数\(z=-1-i(i\)为虚数单位\()\),\(z\)的共轭复数为\(\overline{z}\),则\(|(1-z)·\)\(\overline{z}\)\(|=\)________.
            • 6.

              已知\(z=a+bi(i\)为虚数单位,\(a,b\in R)\),\(\left( 1+i \right)\left( 1-ai \right)=b+2i\),则\(\left| z \right|=(\)   \()\)

              A.\(3\)         
              B.\(\sqrt{5}\)
              C.\(\sqrt{2}\)
              D.\(1\)
            • 7.

              若复数\(z\)满足\(z{\left(1+i\right)}^{2}={\left|1+i\right|}^{2} \),则\(z=\) __________.

            • 8.
              已知复数\(z= \dfrac {1+2i}{2-i}(i\)是虚数单位\()\),则\(|z|=\) ______ .
            • 9.

              已知复数\(z=1+i\),则下列命题中正确的个数是

                 \(①|z|=\sqrt{2}\);\(②\overline{z}=1-{i}\);\(③z\)的虚部为\(i\);\(④z\)在复平面内对应的点位于第一象限.

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

              设复数\(z=-1-i(i\)为虚数单位\()\),\(z\)的共轭复数为\( \overset{¯}{z} \),则\(|(1-z)⋅ \overset{¯}{z} |=(\)  \()\)

              A.\( \sqrt{10} \)
              B.\(2\)
              C.\( \sqrt{2} \)            
              D.\(1\)
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