Ta có: \({z^2} = {(a + bi)^2} = {a^2} - {b^2} + 2abi\)
\({(\bar z)^2} = {(a - bi)^2} = {a^2} - {b^2} - 2abi\)
a) \({z^2} + {\left( {\overline z } \right)^2}\) \( = {a^2} - {b^2} + 2abi + {a^2} - {b^2} - 2abi\) \( = 2\left( {{a^2} - {b^2}} \right)\).
b) \({z^2} - {\left( {\overline z } \right)^2}\)\( = {a^2} - {b^2} + 2abi - {a^2} + {b^2} + 2abi\)\( = 4abi\).
c) \({z^2}.{\left( {\overline z } \right)^2} = {\left( {z.\overline z } \right)^2} = {\left( {{a^2} + {b^2}} \right)^2}\).
