Complex Conjugate Calculator
This calculator finds the complex conjugate of any complex number. It’s a useful tool in algebra, engineering, signal processing, and complex analysis, where conjugates are used to simplify expressions or solve equations involving complex numbers.
Find the Conjugate of a Complex Number
Complex Conjugate Formula
$$\text{If } z = a + bi,\ \text{then the complex conjugate is } \bar{z} = a – bi$$
Explanation:
To find the conjugate of a complex number, simply change the sign of the imaginary part. This operation reflects the number across the real axis on the complex plane.
Complex Conjugate – Calculation Example
z = 5 + 3i
Conjugate: 5 – 3i
z = -2 – 7i
Conjugate: -2 + 7i
Complex conjugates are used in rationalizing denominators, finding moduli, and solving complex equations. In electrical engineering and physics, they simplify calculations involving impedance, power, and waveforms. This calculator provides fast, accurate conjugates for any complex input.