The additive inverse of a complex number is obtained by negating both the real and imaginary parts of that number. A complex number is typically expressed in the form a + bi, where a represents the real part and b represents the imaginary part.
In this case, the complex number given is 8 + 3i. To find its additive inverse, we follow these steps:
- Identify the real part, which is 8.
- Identify the imaginary part, which is 3i.
- Negate the real part: -8.
- Negate the imaginary part: -3i.
Therefore, the additive inverse of 8 + 3i is -8 – 3i.
This result means that when you add 8 + 3i and its additive inverse -8 – 3i, the sum will always equal zero:
(8 + 3i) + (-8 – 3i) = 0 + 0i = 0.
In summary, the additive inverse of the complex number 8 + 3i is -8 – 3i.