Calculadora de Conjugado Complexo

This complex conjugate calculator takes a complex number in the form a + bi (with a and b real) and returns its conjugate (a - bi) and its modulus (|z| = √(a² + b²)). The conjugate is obtained by flipping the sign of the imaginary part, while the modulus represents the distance from the point (a, b) to the origin in the complex plane.

The calculation is straightforward: for z = a + bi, the conjugate is a - bi and the modulus is the square root of the sum of squares of the real and imaginary parts. This tool is useful in subjects like linear algebra, signal processing, and physics, where complex numbers are common.

Use this calculator when you need the conjugate to simplify division of complex numbers, compute powers, or verify properties such as z * z̄ = |z|^2. It is also helpful for students checking exercises or teachers preparing examples.

Be careful: the conjugate only changes the sign of the imaginary part; the real part remains the same. Also, the modulus is always a non-negative real number. Ensure you input values correctly, especially if the imaginary part is negative (e.g., 3 - 2i should be entered as a=3, b=-2).