📘 Operations with Complex Numbers – Complete Algebra 2 Workbook 💡 Overview

This comprehensive 12-chapter workbook guides students step-by-step through every major concept of complex numbers — from the fundamentals to advanced applications like De Moivre’s theorem and signal analysis.
Each chapter includes

• 5 fully solved exercises with detailed solutions
  
• 15 practice problems for mastery
  
• A complete answer key
  

Perfect for Algebra 2, Pre-Calculus, College Algebra, or introductory Complex Analysis courses.

📚 Table of ContentsChapter 1 – Complex Number Basics

• Rectangular, polar, and trigonometric forms
  
• Modulus, argument, and conjugates
  
• Conversion between forms
  

Chapter 2 – Addition & Subtraction I — Rectangular Form

• Component-wise addition and subtraction
  
• Geometric interpretation as vector operations
  

Chapter 3 – Addition & Subtraction II — Translations and Conjugates

• Effects of real and imaginary shifts
  
• Relationships between conjugates
  

Chapter 4 – Multiplication I — Rectangular Form

• FOIL method and distributive property
  
• Products with conjugates
  
• Special identities
  

Chapter 5 – Multiplication II — Polar/Trigonometric Form

• Multiplying moduli and adding arguments
  
• Geometric interpretation as rotation and scaling
  

Chapter 6 – Division I — Rectangular Form (Using Conjugates)

• Rationalizing denominators
  
• Finding reciprocals
  
• Simplifying quotients
  

Chapter 7 – Division II — Polar/Trigonometric Form

• Dividing moduli and subtracting arguments
  
• Converting between forms
  

Chapter 8 – Powers via De Moivre’s Theorem

• Computing powers of complex numbers
  
• Negative and fractional exponents
  
• Applications of De Moivre’s theorem
  

Chapter 9 – Quotients, Products, and Mixed Forms

• Hybrid operations combining polar and rectangular forms
  
• Simplification strategies
  

Chapter 10 – Order of Operations & Simplification

• Combining multiple operations correctly
  
• Mixed expressions with conjugates and powers
  

Chapter 11 – Applications to Algebraic Equations

• Solving equations with complex coefficients
  
• Systems of complex linear equations
  

Chapter 12 – Applications to Geometry & Signals

• Rotations, reflections, and scaling in the complex plane
  
• Basic electrical and signal interpretations
  

🧩 What’s Included

✔ 12 chapters of scaffolded instruction
✔ Over 200 exercises (with 60 fully solved examples)
✔ Clear, consistent layout for classroom or independent study
✔ Comprehensive answer key at the end

🎯 Perfect For

• High school and college teachers looking for ready-to-print lessons
  
• Students needing extra practice and conceptual clarity
  
• Tutors and homeschoolers teaching advanced algebra topics
  

✨ Product Details

• File format: PDF
  
• Pages: Approx. 150+
  
• Language: English
  
• Author: Wafa Bounab
  
• Copyright © 2025 Math Master Worksheets