Complex Number Argument Calculator

Easily calculate the argument (or phase) of a complex number. Enter the real and imaginary parts below to visualize and find the argument in radians and degrees.

Input Complex Number

Re =
Im =

Result

Argument (in radians):

Complex Number Visualization

Understanding Complex Number Arguments

In mathematics, a complex number can be graphically represented on a complex plane, with the real part along the x-axis and the imaginary part along the y-axis. The argument of a complex number is the angle between the positive real axis and the vector joining the origin to the complex number point. It's also known as the phase of the complex number.

The argument is typically measured in radians or degrees. The principal value of the argument is usually taken to be in the interval (−π, π] radians or (−180°, 180°] degrees.

This calculator helps you find the argument of any complex number you input, and visualizes it on the complex plane, making it easier to understand this concept. You can use this tool for educational purposes, complex number analysis, and more.