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소개

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.

공식

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.

단계별 안내

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

실제 예시

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.

자주 묻는 질문

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.