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The additive inverse is were if you add the number an its opposite it become zero, so therefore this would show you that the opposite of this number is -9+4i , to help remember what a additive inverse is just think of how a inverse is like a opposite an remember that the inverse plus your number will equal zero.

I hope this helps.

Answer:  The additive inverse of the given complex number is [tex]-9+4i.[/tex]

Step-by-step explanation:  We are given to find the additive inverse of the following complex number :

[tex]z=9-4i.[/tex]

We know that

the complex number z' is the additive inverse of a complex number z, if

[tex]z+z'=0.[/tex]

So, let z' be the additive inverse of the given complex number z.

Then, we must have

[tex]z+z'=0\\\\\Rightarrow (9-4i)+z'=0\\\\\Rightarrow z'=0-(9-4i)\\\\\Rightarrow z'=-9+4i.[/tex]

Thus, the additive inverse of the given complex number is [tex]-9+4i.[/tex]

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