Complex Linear Mapping Diagrams I (Circles)
Mapping diagram for linear complex function. I
A complex linear function where has some qualities similar to a real linear function, but when is a complex number, there is a distinct geometric feature: the function magnifies by |b| while rotating the result, in the plane by and then translating that result by the vector corresponding to . This process is sometimes described as a translated amplitwist.
The mapping diagram can be used to understand this visually.
Check the box Hide/show MD of function.
- Move the complex number b in the control frame on the horizontal axis to see how the magnification works.
- Move the complex number b off the horizontal to see how the amplitwist works.
- Move the complex number a in the control frame to see how the translation works.
Mapping diagram for linear complex function. I
A complex linear function where has some qualities similar to a real linear function, but when is a complex number, there is a distinct geometric feature: the function magnifies , by |b| while rotating the result, in the plane by and then translating that result by the vector corresponding to . This process is sometimes described as a translated amplitwist.
The mapping diagram can be used to understand this visually.
Check the box Hide/show MD of function.
- Move the complex number b in the control frame on the horizontal axis to see how the magnification works.
- Move the complex number b off the horizontal to see how the amplitwist works.
- Move the complex number a in the control frame to see how the translation works.
Use the slider to change the radius of the circle, r, in the domain for the mapping diagram.