知识点挑题 - 高中数学 - 优优班--学霸训练营

2．

若\(z=4+3i(i\)为虚数单位\()\)，则\(\dfrac{{\bar{z}}}{\left| {\bar{z}} \right|}=(\)　　\()\)

A．\(\dfrac{3}{5}-\dfrac{4i}{5}\)

B．\(\dfrac{3}{5}+\dfrac{4i}{5}\)

C．\(\dfrac{4}{5}+\dfrac{3i}{5}\)

D．\(\dfrac{4}{5}-\dfrac{3i}{5}\)

难度：中等

3．

设\(z=\dfrac{1-{i}}{1+{i}}+2{i}\)，则\(\left| z \right|=\)( )

A．\(0\)

B．\(\dfrac{1}{2}\)

C．\(1\)

D．\(\sqrt{2}\)

难度：中等

4．

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

A．若\(|z_{1}|=|z_{2}|\)，则\(z_{1}^{2}=z_{2}^{2}\)

B．若\({{z}_{1}}=\overline{{{z}_{2}}}\)，则\(\overline{{{z}_{1}}}={{z}_{2}}\)

C．若\(|z_{1}|=|z_{2}|\)，则\({{z}_{1}}\cdot \overline{{{z}_{1}}}={{z}_{2}}\cdot \overline{{{z}_{2}}}\)

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

难度：中等

5．

设\(i\)是虚数单位，\(\overline{z}\)表示复数\(z\)的共轭复数\(.\)若\(z=1-2i\)，则复数\(z+i\cdot \overline{z}\)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

难度：中等

6．

若\(z=4+3i(i\)为虚数单位\()\)，则\(\dfrac{{\bar{z}}}{\left| {\bar{z}} \right|}=(\)　　\()\)

A．\(\dfrac{3}{5}-\dfrac{4i}{5}\)

B．\(\dfrac{3}{5}+\dfrac{4i}{5}\)

C．\(\dfrac{4}{5}+\dfrac{3i}{5}\)

D．\(\dfrac{4}{5}-\dfrac{3i}{5}\)

难度：中等