By Kardi Teknomo, PhD .
ComplexNumber


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There are two ways to represent a point in a plane. One way is using Cartesian coordinate and the other way is using polar coordinate. Using Cartesian coordinate, a complex number is represented as a single point in the complex plane, Complex Number Tutorial: Magintude and Direction? . Using Polar coordinate, a complex number is represented as a vector with magnitude and direction.

Complex Number Tutorial: Magintude and Direction? Complex Number Tutorial: What is Complex Number?

The direction is measured as an angle in radians. Positive angle is measured counterclockwise from the positive real axis. The directed angle is called argument of the complex number.

Complex Number Tutorial: What is Complex Number?

The magnitude of a complex number is the length of vector Complex Number Tutorial: What is Complex Number? . The magnitude is sometimes called amplitude , modulus or absolute value of complex number Complex Number Tutorial: Magintude and Direction? .

Complex Number Tutorial: What is Complex Number?

The direction of vector Complex Number Tutorial: Magintude and Direction? is given by

Complex Number Tutorial: What is Complex Number?

We can also write for the angle itself as argument of the complex number Complex Number Tutorial: What is Complex Number?

Complex Number Tutorial: What is Complex Number?

Note that you must care about the quadrant in which the complex number lies by computing the correct signed value of the angle.

Complex Number Calculator

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

Properties

  • Real part inequalities Complex Number Tutorial: What is Complex Number? . It will become equal when the imaginary parts is zero.
  • Imaginary part inequality Complex Number Tutorial: Magintude and Direction? . It will become equal when the real parts is zero.

See Also : Complex Conjugate , Arithmetic of Complex Number

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