What is the additive inverse of the complex number9−4i9-4i9−4i?

Step 1: Define the Problem

Identify the additive inverse of the complex number $9 - 4i$.

Step 2: Break Down the Problem

The additive inverse of a complex number $a + bi$ is $-a - bi$. This is because when you add a number to its additive inverse, the result is zero.

Step 3: Apply Relevant Concepts

For the complex number $9 - 4i$, the additive inverse is calculated as follows:

• Change the sign of the real part: $-9$
• Change the sign of the imaginary part: $+4i$

Step 4: Analysis, Verify and Summarize

Verify by adding the original number and its additive inverse: $(9 - 4i) + (-9 + 4i) = 0$ This confirms that the calculation is correct.

Final Answer

The additive inverse of the complex number $9 - 4i$ is $-9 + 4i$.