For all z `in` C, prove that
(i) `(1)/(2)(z+bar(z))=Re(z),`
(ii) `(1)/(2i)(z-bar(z))=Im(z),`
(iii) `z bar(z)=|z|^(2),`
(iv) `z+bar(z))"is real",`
(v) `(z-bar(z))"is 0 or imaginary".`