What is the additive inverse of the complex number 9 - 4i?
-9 - 4i, -9 + 4i, 9 - 4i, 9 + 4i

Solution:

The additive inverse identity of complex numbers says that there exists a unique complex number -z for z such that z + (-z) = 0.

⇒ -(9 - 4i) = -9 + 4i.

If z = 9 - 4i, then -z = -9 + 4i

z + (-z) = 0

⇒ 9 - 4i + (-9 + 4i) = 0

Example: Let z = x + iy, then -z = -(x + iy)

By using the additive inverse identity of the complex numbers,

⇒ x + iy + (-x - iy) = 0

Hence, the additive inverse of the complex number 9 - 4i is -9 + 4i.

What is the additive inverse of the complex number 9 - 4i?

Summary:

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