By Kardi Teknomo, PhD .
ComplexNumber


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A conjugate of a complex number Complex Conjugate is defined as

Complex Conjugate

The number Complex Conjugate and Complex Conjugate differ only in the sign of the imaginary part. The real parts are the same.

Example

Complex Conjugate then Complex Conjugate

Representing in polar form, if Complex Conjugate then Complex Conjugate

  • The magnitude is Complex Conjugate
  • The direction is Complex Conjugate . Note the argument of the results must be reduced mod Complex Conjugate to values in the range of 0 to Complex Conjugate .

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 Conjugate

Complex Number Calculator

First number: real part imaginary part Second number: real part imaginary part Operation

Properties

The following are useful properties of conjugate complex:

  • A conjugate complex of a conjugate return the complex number itself Complex Conjugate
  • Addition of complex conjugate Complex Conjugate
  • Subtraction of complex conjugate Complex Conjugate
  • Multiplication of complex conjugate Complex Conjugate
  • Division of complex conjugate Complex Conjugate
  • The real part of a complex number can be obtained from Complex Conjugate
  • The imaginary part of a complex number can be obtained from Complex Conjugate
  • Square absolute of a complex number Complex Conjugate

See Also : Arithmetic of Complex Number

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