Question

What is the additive inverse
of the complex number -12 + 4i?

Answer 1

12 - 4i

Explanation:

Additive inverses undo complex numbers.

Additive Inverses

An additive inverse is a number that when added to another equals zero. For example, -2 and 2 are additive inverses. This is because -2 + 2 = 0. This same idea applies to imaginary numbers and complex numbers. Additive inverses are also known as opposite. To return to the first example, -2 and 2 could also be called opposites.

Finding the Additive Inverse

In order to find the additive inverse, all you need to do to is flip the sign of the numbers. If a number is positive, then make it negative, and vice versa. In the complex number -12 + 4i, -12 is negative and 4i is positive. So, we need to flip their signs.

• 12 - 4i

We can check our work by adding them together and seeing if the sum is 0.

• (-12 + 4i) + (12 - 4i) = 0

So, 12 - 4i is the additive inverse of -12 + 4i.