VIC: Imaginary Explosions

Objectives

• Number systems and recursion
• Representation of complex numbers
• Arithmetic of complex numbers in Cartesian form
• Algorithms for computation in a variety of contexts.

Vocabulary

• Imaginary
• Real component
• Imaginary component
• Argand Plane

About the Lesson

Using only addition and multiplication of complex numbers, students conduct an exploration into the patterns (Julia Sets) generated by complex numbers. The activity works through checking if numbers get bigger or smaller under repeated multiplication. The second and third stage has students adding a constant to the 'mix'. The dynamic nature of TI-Nspire makes this activity particularly interesting as the graphs update very quickly and the animations can be somewhat unexpected.