Additive inverse of a complex number

The additive inverse of a complex number a + bi is the complex number x + yi such that a + bi + x + yi = 0

Solve for x and y using a + bi + x + yi = 0

a + bi + x + yi = 0

Subtract x from each side of the equation

a + bi + x - x + yi = 0 - x

a + bi + yi = 0 - x

Subtract yi from each side of the equation

a + bi + yi - yi = 0 - x - yi

a + bi = - x - yi

Now, you can compare the real parts and the imaginary parts of a + bi = - x - yi

We get a  = -x and b = -y

When a = -x, x = -a

When b = -y, y = -b

The additive inverse is x + yi = -a + -bi

Other examples showing how to find the additive inverse of a complex number


Example #1:

Find the additive inverse of 4 + -5i

The additive inverse of 4 + 5i is the complex number x + yi such that

4 + -5i + x + yi = 0

4 + -5i = - x - yi

Compare the real parts and the imaginary parts of 4 + -5i = - x - yi

We get -x = 4 and -y = -5

When -x = 4, x = -4

When -y = -5, y = 5

The additive inverse of 4 + -5i is the complex number -4 + 5i 

Example #2:

Find the additive inverse of -2 + -6i

The additive inverse of -2 + -6i is the complex number x + yi such that

-2 + -6i + x + yi = 0

-2 + -6i = - x - yi

Compare the real parts and the imaginary parts of -2 + -6i = - x - yi

We get -x = -2 and -y = -6

When -x = -2, x = 2

When -y = -6, y = 6

The additive inverse of -2 + -6i is the complex number 2 + 6i 

Recent Articles

  1. Write a Polynomial from Standard Form to Factored Form

    Oct 14, 21 05:41 AM

    Learn how to write a polynomial from standard form to factored form

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.