Proof that the additive inverse of a complex number (imaginary number is its negative counterpart – just as it is in the Real numbers.
The real part (one side) must equal the real part of the other side, and the coefficients of the imaginary parts of both sides must be equal. this gives us
a + c + (b + d)i = 0 + 0i -> a + c = 0 and b + d = 0 -> c=-a d=-b
the additive inverse of z was defined as as c+di. –> F = -a +(-b)i -> F=-a-bi
this proves that the additive inverse of any complex number z = a + bi is equal to -a – bi
If z = a + bi, the addiitive inverse (minus z) must be -(a+bi) = -a-bi which holds TRUE
So multiplying a complex number by -1 results in the additive inverse of the complex number – just like it does with real numbers.
The additive inverse of the complex number z = a + bi where 
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