A conjugate of a complex number is defined as
The number and differ only in the sign of the imaginary part. The real parts are the same.
Representing in polar form, if then
- The magnitude is
- The direction is . Note the argument of the results must be reduced mod to values in the range of 0 to .
Graphically a conjugate complex is the reflection a complex number with respect to the real axis. Drawing below illustrates a complex number and its conjugate.
Complex Number Calculator
The following are useful properties of conjugate complex:
- A conjugate complex of a conjugate return the complex number itself
- Addition of complex conjugate
- Subtraction of complex conjugate
- Multiplication of complex conjugate
- Division of complex conjugate
- The real part of a complex number can be obtained from
- The imaginary part of a complex number can be obtained from
- Square absolute of a complex number
See Also : Arithmetic of Complex Number