Phase 3: Advanced Math for AI · ~60 minutes · Python

Complex Numbers for AI

The square root of -1 is not imaginary. It is the key to rotations, frequencies, and half of signal processing.

What you will learn

Perform complex arithmetic (add, multiply, divide, conjugate) in both rectangular and polar form
Apply Euler's formula to convert between complex exponentials and trigonometric functions
Implement the Discrete Fourier Transform using complex roots of unity
Explain how complex rotations underlie RoPE and sinusoidal positional encodings in transformers

Introduction

Type: Learn
Language: Python
Prerequisites: Linear Algebra Intuition, Calculus for Machine Learning
Time: ~60 minutes

Objective

Learning objectives

Perform complex arithmetic (add, multiply, divide, conjugate) in both rectangular and polar form
Apply Euler's formula to convert between complex exponentials and trigonometric functions
Implement the Discrete Fourier Transform using complex roots of unity
Explain how complex rotations underlie RoPE and sinusoidal positional encodings in transformers

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build, Check Yourself, Key Terms & Next — plus a hands-on lab, quiz, and project artifact.

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