Online graphically sum of complex numbers

Addition and difference of the complex numbers z1 and z2

The operation with the complex numbers is graphically presented. The resulting sum is given by the red vector. By moving the vector endpoints the complex numbers can be changed. The dotted lines are the parallel moved vectors.

z1 = x1 + i y1
z2 = x2 + i y2
Sum / Difference
+ i 
+ i 
Polar co-ordinates

Axes ranges


Complex numbers


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).

Addition and subtraction of complex numbers

The addition and subtraction of complex numbers corresponding to the addition and subtraction of the position vectors. That the real and imaginary components are added or subtracted.

With z1 = x1 + i y1 and z2 = x2 + i y2 is

z1 + z2 = x1 + x2 + i ( y1 + y2 )

z1 - z2 = x1 - x2 + i ( y1 - y2 )

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