Additive Inverse of Complex Numbers

Introduction to Complex numbers:

Complex number is said to be the sum of whole numbers and imaginary numbers. The imaginary numbers can be denoted as in numbers in form of ‘’i’’, where the value of I is `sqrt(-1)` . In this article, we see about the additive inverse of complex numbers. The additive inverse of the any number is the changing the sign of the number. That is instead –ve sign is positive and vice versa.

Additive Inverse of Complex Numbers:

We know that the sum of any number and its additive inverse of that number is zero.

To find: Additive Inverse of the Complex Numbers:

Let take the complex numbers Z = X + iy and its inverse be Z-1 = a + ib

Step 1: Now add the Z and Z-1, we get

Z + Z-1 = (X + iy) + (a + ib) = 0

Step 2: Combine Like term, we get

(X + a) + i (y + b) = 0

Step 3: By using zero product property, we can equating as

X + a = 0 and i (y + b) = 0

X = -a and y = -b

Thus the additive inverse of the complex numbers X + iy = -X – iy

Example Problems – Additive Inverse of Complex Numbers:

Example 1:

Choose the correct option - The additive inverse of the complex number 5 + 6i

Option:

a)     5 – 6i

b)    -5 + 6i

c)     -5 – 6i

d)    -11i

Solution:

Given: 5 + 6i

Formula: The additive inverse of X + iy = - X – iy

5 + 6i = -5 – 6i

Answer: Option c

Example 2:

What is the value of the sum of the complex number 4 + 8i and its additive inverse?

Solution:

Given: The sum of 4 + 8i and its additive inverse

The additive inverse of 4 + 8i = -4 – 8i

4 + 8i – 4 -8i = (4 -4) + i (8 -8) = 0

Answer: 0

Is this topic Is 0 a Rational Number? hard for you? Watch out for my coming posts.

Practice Problem – Additive Inverse of Complex Numbers:

Problem 1;

What is the additive inverse of the complex numbers 7 – 9i?

Answer: -7 + 9i

Problem 2:

What is the sum of any complex numbers and its additive inverse?