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Prove that: (i) R(e)(z(1)z(2))=R(e)(z1...

Prove that:
(i) `R_(e)(z_(1)z_(2))=R_(e)(z_1)R_(e)(z_(2))-I_(m)(z_(1))I_(m)(z_(2))`
(ii) `I_(m)(z_(1)z_(2))=R_(e)(z_(1))I_(m)(z_(2))+R_(e)(z_(2))I_(m)(z_(1))`.

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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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