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Kalkulator pierwiastków zespolonych

Znajdź zespolone pierwiastki równania kwadratowego lub pierwiastki z jedności.

Wprowadzenie

Complex Roots Calculator — Find complex roots of a quadratic or roots of unity. Enter a, b, c, Roots of unity n (0 = use quadratic instead) to get an instant, accurate result.

Wzór

Quadratic mode: solves ax²+bx+c=0 via the quadratic formula, returning complex roots (−b±i√|d|)/(2a) when the discriminant d is negative. nth-roots-of-unity mode: roots = (cos θ, sin θ) for θ = 2πk/n, k = 0..n−1.

Krok po kroku

  1. Enter the a.
  2. Enter the b.
  3. Enter the c.
  4. Enter the Roots of unity n (0 = use quadratic instead).
  5. Click Calculate to see your result instantly.

Przykład z życia

Example: With a = 1, b = 2, c = 5, Roots of unity n (0 = use quadratic instead) = 0, the Complex Roots Calculator gives X1: -1, 2, X2: -1, -2, Complex: yes.

Często Zadawane Pytania

What are roots of unity?
The n complex numbers that, raised to the power n, equal 1 — evenly spaced around the unit circle.
When does the quadratic give complex roots?
Whenever the discriminant b²−4ac is negative.
What inputs does the Complex Roots Calculator need?
You'll need to provide: a, b, c, Roots of unity n (0 = use quadratic instead). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Complex Roots Calculator?
The Complex Roots Calculator applies the formula exactly as calculated — Quadratic mode: solves ax²+bx+c=0 via the quadratic formula, returning complex roots (−b±i√|d|)/(2a) when the discriminant d is negative. nth-roots-of-unity mode: roots = (cos θ, sin θ) for θ = 2πk/n, k = 0..n−1. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Complex Roots Calculator free to use?
Yes, the Complex Roots Calculator is completely free, requires no signup, and runs instantly in your browser.

O Kalkulator pierwiastków zespolonych

The Complex Roots Calculator uses a real, verifiable formula — Quadratic mode: solves ax²+bx+c=0 via the quadratic formula, returning complex roots (−b±i√|d|)/(2a) when the discriminant d is negative. nth-roots-of-unity mode: roots = (cos θ, sin θ) for θ = 2πk/n, k = 0..n−1. — so results are accurate every time, not an approximation.