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.

Example

then

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

### Properties

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The following are useful properties of conjugate complex:
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- 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

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See Also
**
:
Arithmetic of Complex Number

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