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Complex numbers formulas
10 formulas for Complex numbers, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Imaginary unit | i² = −1; i³ = −i; i⁴ = 1 | |
| Form | z = a + ib | |
| Modulus | |z| = √(a² + b²) | |
| Argument | arg z = tan⁻¹(b/a) | adjust for quadrant |
| Conjugate | z̄ = a − ib; z·z̄ = |z|² | |
| Polar form | z = r(cos θ + i sin θ) = re^(iθ) | |
| De Moivre | (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ | |
| Euler | e^(iθ) = cos θ + i sin θ | |
| Cube roots of unity | 1, ω, ω²; 1 + ω + ω² = 0; ω³ = 1 | |
| Triangle inequality | |z₁ + z₂| ≤ |z₁| + |z₂| |
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