Question

What is the additive inverse of the complex number -8 + 3i?

Answer 1

The additive inverse of a number x is a number y such that

`x+y=0`

From this definition, we can derive

`y=-x`

So, to get the additive inverse of a number, you simply have to switch its signs.

Since complex numbers are made of two pieces (real and complex parts), you'll have to switch both signs:

`z=-8+3i \implies -z = 8-3i`

In fact, if you try to sum them, you have

`(-8+3i)+(8-3i)=(-8+8)+(3i-3i)=0`

Answer 2

8 - 3i

Explanation:

The additive inverse is what you add to a number to get zero.

Thus adding 8 - 3i to - 8 + 3i gives

- 8 + 3i + 8 - 3i = 0

Additive inverse is 8 - 3i