Complex numbers

Calculation rules

Addition: u = z1 + z2= (x1+ i y1 ) + (x2 + i y2 ) = (x1 + x2 ) + i (y1 + y2 )

Simulation

A quadratic 10x10 point array of edge length 1 is grouped in the z plane . One edge point is colored in red and connected to the origin by a red vector. One can shift the array by drawing the red point with the mouse to any position in the plane.

The size of the array can be decreased by a slider until just the red point is visible. This allows you to experiment with a single point. The scale of the coordinate system is adjusted to the size of the array.

A second point (green vector) is added to every point in the array. By drawing the blue arrowhead with the mouse, the absolute size and direction of the green vector can be changed.

In the u plane the result of the addition is displayed. The green vector is shifted in blue to the arrowhead of the red edge vector with its original direction, resulting in the gray sum vector from the origin to the red edge point.

A blue copy of the red vector complements the scheme to a parallelogram, as is familiar for vector addition.

The reset button resets to the default position.