Complex Numbers

Complex Numbers and Functions

Phase 1: The Foundations

Syllabus Goal

Study elements of complex analysis. Master Euler’s formula and basic complex algebra.

Core Concepts

  • Definition: $z = x + iy$.
  • Polar Form: $z = r(\cos \theta + i \sin \theta) = re^{i\theta}$.
  • Euler’s Formula: $e^{i\theta} = \cos \theta + i \sin \theta$.

Key Operations

  1. Addition/Subtraction: $(a+bi) \pm (c+di) = (a\pm c) + (b\pm d)i$.
  2. Multiplication: $(a+bi)(c+di) = (ac-bd) + (ad+bc)i$.
  3. Division: Multiply numerator and denominator by the conjugate of the denominator.

Implementation in Zig

  • Using std.math.Complex for complex number arithmetic.
  • Implementing Euler’s formula visualization.