Complex-plane transformations

Try it step by step

1. Enter a finite complex value or a defined complex parameter.
2. Choose a transformation.
3. For translation or multiplication, enter the real and imaginary parts of a.
4. Inspect the vectors and values; add the transformed value or show complex values on the main graph.

Options explained

Translate

Adds a to z.

Rotate/scale

Multiplies z by a, changing its direction and magnitude.

Reflect

Takes the complex conjugate.

Square

Calculates z².

Reciprocal

Calculates 1/z; zero has no reciprocal.

Modulus / argument

The tool shows magnitude and angle; angle units follow the document mode. The argument of zero is undefined.

Add transformed value

Adds the calculated value as a new expression.