# Polar form of complex number

Calculator and for calculating the polar form of a complex number

## Polar form of a complex number

Enter a complex number to calculate the polar shape. The result can be displayed in degrees or radians.

Polar form calculater

 Input Complex number + i Decimal places 0 1 2 3 4 6 8 10 Results Magnitude Angle Angle measure Degree Radian

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).