Enter a complex number to calculate the polar shape.
The result can be displayed in degrees or radians.
Polar form calculater
Magnitude r = 2 Angle φ = 45°
Description of the polar form of a complex number
Every complex number \(z\) can be represented as a vector in the Gaussian number plane.
This vector is uniquely defined by the real part and the imaginary part of the complex number \(z\).
A vector emanating from the zero point can also be used as a pointer.
This pointer is uniquely defined by its length and the angle \(φ\) to the real axis.
Positive angles are measured counterclockwise, negative angles are clockwise.
A complex number can thus be uniquely defined in the polar form by the pair \((|z|, φ)\). \(φ\) is the angle belonging to the vector.
The length of the vector \(r\) equals the magnitude or absolute value \(|z|\) of the complex number.
The general notation \(z = a + bi\) is called normal form (in contrast to the polar form described above).