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Define addition and multiplication of tw...

Define addition and multiplication of two complex numbers `z_(1) and z_(2)`. Hence show that:
(i) `R_(e)(z_(1)+z_(2))=R_(e)(z_(1))+R_(e)(z_(2))`
(ii) `I_(m)(z_(1)+z_(2))=I_(m)(z_(1))+I_(m)(z_(2))`
(iii) `R_(e)(z_(1)z_(2))=R_(e)(z_(1))R_(e)(z_(2))-I_(m)(z_(1))I_(m)(z_(2))`
(iv) `I_(m)(z_(1)z_(2))=R_(e)(z_(1))I_(m)(z_(2))+I_(m)(z_(1))R_(e)(z_(2))`.

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