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Chapter 1

Complex Numbers

The new number system — complex numbers, their operations, trigonometric form, and roots.

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1.1 The Need for a New Number System

The Imaginary Unit and i²Easy

1.2 Complex Numbers and Their Operations

Complex Numbers in Standard FormEasy
Adding and Subtracting Complex NumbersMedium
Multiplying Complex NumbersMedium
Dividing Complex Numbers Using ConjugatesMedium

1.3 The Complex Plane and Trigonometric Form

The Complex Plane and ModulusMedium
The Trigonometric (Polar) Form of a Complex NumberMedium

1.4 De Moivre's Theorem and Roots of Complex Numbers

De Moivre's TheoremHard
Finding nth Roots of a Complex NumberHard

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