Lesson 1.14

Adding & Subtracting Complex Numbers

If you can combine like terms (), you can add complex numbers. It's the exact same logic!

Introduction

Combining complex numbers is intuitive. You simply treat like any other variable.

Past Knowledge

.

Today's Goal

Apply this to .

Future Success

This separation of Real and Imaginary components is used heavily in physics (resultant forces).

Key Concepts

1. Adding Complex Numbers

Combine the Real parts together, and the Imaginary parts together.

2. Subtracting Complex Numbers

You MUST distribute the negative sign to both terms in the second parenthesis.


Then combine like terms as usual.

Worked Examples

Example 1: Addition

Basic

Simplify .

1

Group Real and Imaginary

2

Combine

Result:

Example 2: Subtraction

Intermediate

Simplify .

1

Distribute Negative

2

Combine Like Terms

Example 3: Multiple Terms

Advanced

Simplify .

1

Distribute Negatives

2

Identify Parts

Real: . Imaginary: .

Result:

Common Pitfalls

Sign Errors

Subtracting a negative becomes a positive!

Don't Multiply

is addition, NOT multiplication. Do not FOIL.

Real-Life Applications

In Physics, this is exactly the same as adding vectors or forces. If you walk 3 miles East and 4 miles North, then 2 miles East and 1 mile South, you just add the Easts (Real) and the Norths (Imaginary) separately to find your final position.

Practice Quiz

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