Multiplying complex numbers rotates and scales
Two complex numbers, z = 1 + i and w = 0.5 + 1.5i, are plotted on the complex plane and multiplied together. The animation shows that the product's modulus equals |z| times |w| and its argument equals the sum of the two arguments, verified with actual coordinates. A final check confirms i times i equals two quarter-turns, landing on -1, linking multiplication to combined scaling and rotation. Useful for students learning polar form of complex numbers.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
z = 1 + i and w = 0.5 + 1.5i on the complex plane: their product has modulus |z||w| and argument arg z + arg w, checked numerically, so i times i is two quarter-turns.
Make the next one in this series
- Show De Moivre's theorem by animating repeated powers of a complex number rotating around the origin.
- Visualize division of complex numbers as subtracting arguments and dividing moduli.
- Animate the roots of unity as evenly spaced points on the unit circle.
