By Kardi Teknomo, PhD .
ComplexNumber


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If we have two complex numbers Complex Number Tutorial: Complex Division and Complex Number Tutorial: Complex Division then we can divide one complex number from another complex number.

Complex Number Tutorial: Complex Division

Division of two complex numbers is done by rationalization. Rationalization means multiplying both numerator and denominator by the conjugate of the denominator.

Representing in polar form, if Complex Number Tutorial: Complex Division and Complex Number Tutorial: Complex Division then

Complex Number Tutorial: Complex Division

  • The magnitude is Complex Number Tutorial: Complex Division . Division of two complex number produces magnitude of the length ratio of the two factors.
  • The direction is Complex Number Tutorial: Complex Division . Division of two complex number produces difference of angles of the two factors.

Note the argument of the results must be reduced mod Complex Number Tutorial: Complex Division to values in the range of 0 to Complex Number Tutorial: Complex Division . to values in the range of 0 to Complex Number Tutorial: Complex Division . .

Graphically, complex division is represented by polar representation illustrated below.

Complex Number Tutorial: Complex Division

Complex Number Calculator

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

Properties of Complex Division

  • The multiplicative inverse of Complex Number Tutorial: Complex Division is Complex Number Tutorial: Complex Division because Complex Number Tutorial: Complex Division . is Complex Number Tutorial: Complex Division because Complex Number Tutorial: Complex Division . because Complex Number Tutorial: Complex Division . .
  • In trigonometric form, Complex Number Tutorial: Complex Division , then Complex Number Tutorial: Complex Division . , then Complex Number Tutorial: Complex Division . .
  • In polar form, If Complex Number Tutorial: Complex Division then Complex Number Tutorial: Complex Division . then Complex Number Tutorial: Complex Division . .
  • Graphically, it is illustrated below.

Complex Number Tutorial: Complex Division

See Also : Complex Multiplication , Complex Arithmetic , Complex Conjugate

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