matematicas visuales visual math

Complex geometric progression

From a complex number we can obtain a geometric progression obtaining the powers of natural exponent (multiplying successively)

The modules of the complex numbers of this progression are in geometric progression and the arguments in arithmetical progression.

The indicated point controls with certain precision the beginning of the progression.

The animation shows the result of these succesive products using a continuous dilative rotation.

Each triangle is similar to the previous one and when being turning around the origin the other two wertices they move by the equiangular spiral that constains all the points of the geometric progression.

LINKS

The product as a complex plane transformation
The multiplication by a complex number is a transformation of the complex plane: dilative rotation.
Geometric sequence
Geometric sequences graphic representations
Equiangular spiral
In an equiangular spiral the angle between the position vector and the tangent is constant.