How to Use Complex Conjugate Calculator
The Complex Conjugate Calculator accepts a complex number such as 3 + 4i, 3 - 4i, a real number, or a pure imaginary number. Enter the value and the Complex Conjugate Calculator returns the conjugate immediately.
The result also shows the original number and z times its conjugate, so the relationship to modulus squared is visible.
Formula & Theory — Complex Conjugate Calculator
The Complex Conjugate Calculator uses the rule z = a + bi and z conjugate = a - bi. The real part a stays unchanged, while the imaginary coefficient b reverses sign.
Multiplying a complex number by its conjugate removes the imaginary part: (a + bi)(a - bi) = a^2 + b^2. The Complex Conjugate Calculator includes this value to make the rule easier to verify.
Use Cases for Complex Conjugate Calculator
Use the Complex Conjugate Calculator for algebra practice, complex division, modulus calculations, signal processing, electrical engineering, and checking homework. The Complex Conjugate Calculator is a quick way to avoid sign mistakes with imaginary terms.