Addition
\((3 + 4i) + (1 + 2i) = 4 + 6i\)
Calculatrice de nombres complexes
Effectuer des opérations sur les nombres complexes et les visualiser sur le diagramme d'Argand (plan complexe)
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
Theory & Formula
Complex numbers extend real numbers to include imaginary numbers (multiples of i, where i² = -1). They are essential in engineering, physics, and advanced mathematics.
Key concepts:
- Rectangular form: z = a + bi
- Polar form: z = r(cos θ + i sin θ) = r∠θ
- Magnitude: |z| = √(a² + b²)
- Argument: θ = arctan(b/a)
- Conjugate: z̄ = a - bi
- Euler's formula: e^(iθ) = cos θ + i sin θ
\(z = a + bi\), where \(i^2 = -1\)
Worked Examples
Multiplication
\((3 + 4i)(1 + 2i) = -5 + 10i\)
Polar Form
\(5 + 0i = 5\angle 0^\circ\), \(0 + 5i = 5\angle 90^\circ\)