Question

what is the additive inverse of the complex number (9 - 4i)?

• (-9 - 4i)
• (-9 + 4i)
• (9 - 4i)
• (9 + 4i)

Explanation:

🆕 New Concept Discovered: Additive Inverse of Complex Numbers
Opposite signs for both parts

Step 1: Understand the additive inverse

The additive inverse of any number \( z \) is the number that, when added to \( z \), yields a sum of zero:

$$ z + (-z) = 0 $$

For a complex number \( z = a + bi \), its additive inverse is found by changing the sign of both the real part and the imaginary part:

$$ -(a + bi) = -a - bi $$

Step 2: Apply to the given complex number

The given complex number is:

$$ 9 - 4i $$

To find its additive inverse, negate the entire expression:

$$ -(9 - 4i) $$

Distribute the negative sign to both terms:

$$ -9 + 4i $$

Answer:

$$ -9 + 4i $$