Chứng minh rằng:
a) \(\overline {({{{z_1}} \over {{z_2}}})} = {{{{\bar z}_1}} \over {{{\bar z}_2}}}\)
b) \(|{{{z_1}} \over {{z_2}}}| = {{|{z_1}|} \over {|{z_2}|}}\)
Hướng dẫn làm bài
Advertisements (Quảng cáo)
a) Giả sử \({{{z_1}} \over {{z_2}}} = z\) . Ta có: \({z_1} = z.{z_2} = > {\bar z_1} = \bar z.{\bar z_2} < = > \bar z = {{{{\bar z}_1}} \over {{{\bar z}_2}}}\)
Vậy \((\overline {{{{z_1}} \over {{z_2}}})} = {{{{\bar z}_1}} \over {{{\bar z}_2}}}\)
b) Tương tự, \(|{z_1}| = |z.{z_2}| = |z|.|{z_2}|\) hay \(|z| = {{|{z_1}|} \over {|{z_2}|}}\) .
Vậy \(|{{{z_1}} \over {{z_2}}}| = {{|{z_1}|} \over {|{z_2}|}}\)