Find the conjugate of a complex number, and its product with the original. Enter the real and imaginary parts.
Conjugate
—
Imaginary sign flipped.Usage Tip
To divide complex numbers, multiply top and bottom by the conjugate of the denominator — it makes the denominator real.
THE MATH
conjugate of a + bi is a − bi
z × conjugate = a² + b² (a real number)
z × conjugate = a² + b² (a real number)
The conjugate flips the sign of the imaginary part.
It is the key to dividing complex numbers and shows up throughout signal processing and quantum mechanics.
It is the key to dividing complex numbers and shows up throughout signal processing and quantum mechanics.
Enter the real part (a) and imaginary part (b).
A number times its conjugate is always real, equal to the modulus squared.
The conjugate has the same modulus as the original.
A number times its conjugate is always real, equal to the modulus squared.
The conjugate has the same modulus as the original.