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 12 + 4i, its additive inverse can be found by negating both the real part and the imaginary part. Therefore, to find the additive inverse:
- The real part: 12 becomes -12
- The imaginary part: 4i becomes -4i
As a result, the additive inverse of 12 + 4i is -12 – 4i. This means that if you add 12 + 4i and -12 – 4i, you will indeed get zero:
(12 + 4i) + (-12 - 4i) = 0