PROPERTIES OF COMPLEX NUMBER
T here are some property of complex number under +, −, ×, ÷ we prove these properties any value of complex number we take variable a₁, b₁,c₁,d₁,e₁, f₁ ADDITION ( + ) complex number multiplication ( i ): closure property (+) when (a₁+b₁) , ( c₁ + d₁ ) ∈ ℂ = (a₁+ b₁)+ ( c₁ + d₁ ) = (a₁ + c₁ ) + (b₁+ d₁ ) ∈ ℂ (say closed + in complex number ) ( ii ): associative property ( + ) once (a₁+b₁) , ( c₁ ,d₁ ) , (e₁ , f₁ ) ∈ ℂ [ ( (a₁+b₁ ) + ( c₁ +d₁ ) ] + (e₁ + f₁ ) = ( (a₁+ c₁ ) + e₁ ( b₁ + d₁ ) + f₁ = [ a₁ + ( c₁ + e₁ ) , b₁ + ( d₁ + f₁) ] as a result of addition is associative in R what is complex plane = (a₁ , b₁) +( c₁ + e₁ ) + ( d₁ + f₁) = (a₁ , b₁) + [( c₁ + d₁ ) + ( e₁ + f₁) ] thence verify (iii) additive identity ( + ) ∀ ( a₁ ,b₁) ∈ ℂ we have ( 0 , 0 ) ∈ ℂ such that ( a₁ , b₁) + ( 0 , 0 ) = ( a₁+0 , b₁+ 0) = ( a₁ , b₁) this