• Complex Analysis
• 1. Complex Numbers
• 1.1. Introduction
• 1.2. Geometry
• 1.3. Polar Coordinates
• 1.4. Euler's Formula
• 1.5. Basic Topology
• 2. Complex Functions
• 3. Complex Differentiation
• 4. Complex Integration
• 5. Cauchy's Theorem
• 6. The Big Five
• 7. Series
• 8. Taylor and Laurent Series
• 9: Poles and Residues
• Historical Tidbits

1.1. Introduction

Ex 1.1.4 (a): Properties of the Imaginary Unit

This is easy. Since i² = -1, we have:

i = i
i² = -1
i³ = i² i = (-1) i = -i
i⁴ = i² i² = (-1) (-1) = 1
i⁵ = i⁴ i = i
i⁶ = i⁴ i² = -1
i⁷ = -i
i⁸ = 1
...

Interactive Complex Analysis, ver. 1.0.0
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Page last modified: May 27, 2022