Calculadora de Raiz Complexa (raiz quadrada de z = a + bi)

The Complex Root Calculator computes the principal square root of complex numbers in the form z = a + bi. Unlike real numbers, where the square root of a negative is undefined, complex numbers always have two square roots. This tool calculates the principal root, which is the one with a positive real part (or, if the real part is zero, the positive imaginary part).

The calculation uses the formula: √(a+bi) = √((r+a)/2) ± i·√((r−a)/2), where r = |z| = √(a² + b²) is the modulus of the complex number. The sign ± depends on the sign of the imaginary part b: if b ≥ 0, use +; if b < 0, use −. The result is displayed in the form x + yi, with up to 10 decimal places.

Use this calculator when you need to extract the square root of a complex number in engineering, quantum physics, signal processing, or pure mathematics. For example, when solving quadratic equations with a negative discriminant, or analyzing AC circuits. The tool is useful for students and professionals working with complex numbers.

Cautions: Ensure the real and imaginary parts are correct. The calculator returns only the principal root; the other root can be obtained by changing the sign of the imaginary part. Remember that the square root of a complex number is not unique, and the result can be verified by squaring it.