The additive inverse of a complex number is simply the number that, when added to the original complex number, results in zero.
For the complex number 8 + 3i, the additive inverse can be found by negating both the real and imaginary parts. This means we change the sign of the real part (8) and the imaginary part (3i).
Thus, the additive inverse of 8 + 3i is -8 – 3i.
To confirm this, we can perform the addition:
(8 + 3i) + (-8 – 3i) = (8 – 8) + (3i – 3i) = 0 + 0i = 0.
This shows that our calculation is correct. In conclusion, the additive inverse of the complex number 8 + 3i is -8 – 3i.