The additive inverse of a complex number is simply the number that, when added to the original number, results in zero.
For the complex number 9 + 4i, the additive inverse can be found by negating both the real and imaginary parts. This means:
– The real part, which is 9, becomes -9.
– The imaginary part, which is 4i, becomes -4i.
So, the additive inverse of 9 + 4i is -9 – 4i.
To confirm, if you add 9 + 4i and -9 – 4i, you get:
(9 + 4i) + (-9 – 4i) = 0 + 0i = 0,
which shows that -9 – 4i is indeed the additive inverse.