Interactive graphical power of the complex number z


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Square and cubic power of a complex number z

The power operation with the complex numbers is graphically presented. By moving the vector endpoint the complex number can be changed.

Number of digits =

Range of the axis with Re: real part and Im: imaginary part of the numbers

Re-min= Re-max=
Im-min= Im-max=

Complex number

z = x + iy = + i

Complex numbers general

The complex numbers are an extension of the real numbers. Many computational rules of real numbers can be applied to complex numbers. The theory of analytic functions dealt with functions of a complex variable.

The Origin of complex numbers is due to the release of algebraic equations. The origin of the theory of imaginary numbers, that is, all numbers whose square is a negative real number, going to the Italian mathematician Gerolamo Cardano and Rafael Bombelli in the 16th Century. The introduction of the imaginary unit i as the new number is attributed to Leonhard Euler.

Gauss plane

The complex numbers are two-dimensional and can be used as vectors in the Gaussian plane of numbers represent. On the horizontal axis (Re) of the real part and on the vertical axis is applied (Im) of the imaginary part of the complex number. Similar to vectors complex numbers can be expressed in Cartesian coordinates (x, y) or polar coordinates (r, φ).


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