Complex Roots Calculator

Complex roots occur when a polynomial equation has no real solutions — the discriminant is negative. The roots come in conjugate pairs: a + bi and a − bi, where i = √(−1).

1. 1For ax² + bx + c = 0: roots = (−b ± √(b²−4ac)) / 2a
2. 2When b²−4ac < 0: roots are complex
3. 3√(negative) = i × √(|negative|)
4. 4Complex roots always appear as conjugate pairs