Given the complex number 9 - 4i, the additive inverse is the number that when added to the original number, would equate to zero. Another term this may be known as is the additive identity. The additive inverse is simply:
(a + bi) = -(a + bi)
Given: 9 - 4i
-(9 - 4i) = -9 + 4i
Therefore, the answer is B.