# Complex multiplication

- Author:
- Susan Addington

- Topic:
- Geometry, Multiplication, Rotation

Drag the blue points to see the effect of multiplying various shapes by a complex number a. The checkboxes show different shapes. The "before" shape is filled in, and is traced by the blue point P. The "after" shape is not filled, and is traced by P'.

This applet shows the function f(z)=az, where a is fixed complex number, and the input is any complex number in the plane.
In coordinates, a=b+ci and z=x+iy. This function can be computed by using the distributive property: az=(b+ci)(x+yi)=(bx-cy)+(cx+by)i. Geometrically, it rotates the point or object by Arg(a) and stretches it out from the origin by a factor of |a|.