ADDITION OF COMPLEX NUMBERS

Addition Of Complex Numbers

To add Complex Numbers, add the similar terms (real and imaginary) algebraically.

More About Addition of Complex Numbers

If parentheses are enclosed, first remove the parentheses; then place the real parts and imaginary parts together, and add.

Examples of Addition of Complex Numbers

To add (8 + 4i) and (1 + 2i), group the like terms and add.
(8 + 1) + (4 + 2) i = 9 + 6i

Video Examples: Addition of Complex Numbers.

Solved Example on Addition of Complex Numbers

Ques: Simplify: (5 - 4i) + (- 1 + 2i)

Choices:

A. 4 – 2i
B. 5 – 4i
C. 4 + 4i
D. – 4 – 2i
Correct Answer: A

Solution:

Step 1: (5 - 4i) + (- 1 + 2i)
Step 2: = (5 - 1) + (- 4 + 2) i [Group the like terms.]
Step 3: = 4 - 2i

Quick Summary

Add the real parts together.
Add the imaginary parts together.
Combine the results to form a new complex number.

\[ z_1 + z_2 = (a + c) + (b + d)i \]

🍎 Teacher Insights

Emphasize the importance of treating 'i' as a variable during addition. Use visual aids like Argand diagrams to represent complex numbers and their addition.

🎓 Prerequisites

Basic Algebra
Real Numbers
Imaginary Numbers

Check Your Knowledge

Q1: Simplify: (3 + 2i) + (1 - i)

A. 4 + i B. 2 + 3i C. 4 - i D. 3 - 2i

Q2: Simplify: (5 - 3i) + (-2 + 3i)

A. 3 B. 3 + 6i C. 7 D. 3 - 6i

Frequently Asked Questions

Q: How do you add complex numbers?
A: Add the real parts together and the imaginary parts together.

Q: What is the real part of a complex number?
A: The real part is the component without the imaginary unit 'i'.

Q: What is the imaginary part of a complex number?
A: The imaginary part is the coefficient of the imaginary unit 'i'.