The online conjugate calculator returns the conjugate of a complex number.

Writing z = a + ib where a and b are real is called algebraic form of a complex number z :

- a is the real part of z;
- b is the imaginary part of z.

When b=0, z is real, when a=0, we say that z is pure imaginary.

The **conjugate of a complex number** `a+i⋅b`, where a and b are reals, is the complex number `a−i⋅b`.

For **calculating conjugate** of the **complex number** following z=3+i,
enter complex_conjugate(`3+i`) or directly 3+i, if the
complex_conjugate button already appears, the result 3-i is returned.

The complex numbers calculator can also determine the conjugate of a complex expression.
To **calculate the conjugate** of the following complex expression z=`(1+i)/(1-i)`,
enter complex_conjugate(`(1+i)/(1-i)`) or directly
(1+i)/(1-i), if the button complex_conjugate already appears, the result -i is returned.

With this function, the calculator allows the **online calculation of the conjugate** of a **complex number**.

complex_conjugate(z), z is a complex number.

complex_conjugate(`1+i`), returns 1-i

See also

- Amplitude of a complex number : amplitude. The amplitude calculator determines the amplitude of a complex number from its algebraic form.
- Solving quadratic equation with complex number : complexe_solve. The complex number equation calculator returns the complex values for which the quadratic equation is zero.
- Complex conjugate calculator : complex_conjugate. The online conjugate calculator returns the conjugate of a complex number.
- Exponential : exp. The function exp calculates online the exponential of a number.
- Properties of a complex number : properties_complex_number. This calculator allows you to determine the properties of a complex number: complex_number, real_part, imaginary_part, complex_modulus, amplitude, complex_conjugate.
- Complex modulus calculator : complex_modulus. The modulus calculator allows you to calculate the modulus of a complex number online.
- Complex number calculator : complex_number. The complex number calculator allows to perform calculations with complex numbers (calculations with i).
- Imaginary part of complex number : imaginary_part. The imaginary part calculator allows you to calculate online the imaginary part of a complex number.
- Real part of complex number : real_part. The real part calculator allows you to calculate online the real part of a complex number.