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Adding and Subtracting Complex Numbers

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Adding and Subtracting Complex Numbers

Study Guide

Key Definition

Complex numbers are in the form $a + bi$ where $a$ is the real part and $b$ is the imaginary part.

Important Notes

Imaginary unit $i$ is defined as $i^2 = -1$
We add or subtract complex numbers by adding or subtracting corresponding real and imaginary parts
The result of addition or subtraction is another complex number

Mathematical Notation

$a + bi$ represents a complex number

The letter $i$ is used to denote the square root of -1

Why It Works

In complex numbers, real and imaginary parts are independent. Therefore, we can add or subtract them separately.

Remember

While adding or subtracting, always match the real part with the real part and the imaginary part with the imaginary part.

Quick Reference

Adding Complex Numbers:$(a + bi) + (c + di) = (a+c) + (b+d)i$

Subtracting Complex Numbers:$(a + bi) - (c + di) = (a-c) + (b-d)i$

Understanding Adding and Subtracting Complex Numbers

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simply add or subtract the real parts and imaginary parts separately.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the result of $(3+4i)+(2-3i)$?

Real-World Problem

Question Exercise

Intermediate

Electrical Engineering Scenario

In electrical engineering, impedance is represented as a complex number. If the impedance of two components are $3 + 4i$ and $2 - 3i$ ohms respectively, what is the total impedance when they are connected in series?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If you add a complex number to its conjugate, what part of the result will be zero?

Challenge Quiz

Single Choice Quiz

Advanced

What is the result of $(3+4i)-(5-7i)$?

Recap

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Review key concepts and takeaways