Polar form of complex number
Calculator and for calculating the polar form of a complex number
The calculator on this page calculates the polar form of a complex number. To calculate and draw the polar shape, enter a complex number and then click the Calculate button.
The result can be displayed in degrees or radians. The angle is the angle between the vector and the positive x-axis.
|
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).
More information about the polar form →
More complex functions
Absolute value (abs) • Angle • Conjugate • Division • Exponent • Logarithm to base 10 • Multiplication • Natural logarithm • Polarform • Power • Root • Reciprocal • Square root •Cosh • Sinh • Tanh •
Acos • Asin • Atan • Cos • Sin • Tan •
Airy function • Derivative Airy function •
Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye •
|
|