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Complex Numbers

Math Experiment Details

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📖 About This Experiment

Complex numbers extend the real number system by including imaginary numbers. Visualize them on the Argand plane (complex plane) where the x-axis represents real parts and the y-axis represents imaginary parts. Explore rectangular form (a + bi) and polar form (r∠θ).

💡 Key Concepts

  • •Real Part: Horizontal component on Argand plane
  • •Imaginary Part: Vertical component (multiplied by i)
  • •Magnitude (Modulus): Distance from origin
  • •Argument (Angle): Angle from positive real axis
  • •i² = -1: Fundamental imaginary unit

🔢 Key Formulas

Rectangular Form
z = a + bi
Polar Form
z = r(cos(θ) + i·sin(θ)) = re^(iθ)
Modulus & Argument
|z| = √(a² + b²)
arg(z) = arctan(b/a)
🚀 Launch Complex Numbers