Student handout: Using Arms to Visualize Complex Numbers (MathBits)
None 2023
Students move their left arm in a circle to trace out the complex plane (Argand diagram). They then explore the rectangular and exponential representations of complex numbers by using their left arm to show given complex numbers on the complex plane. Finally they enact multiplication of complex numbers in exponential form and complex conjugation.
Geometric representation of complex numbers in rectangular \(x+iy\) and exponential \(re^{i\phi}\) forms;
Multiplication of complex numbers in exponential form adds the phases;
Complex conjugation is a reflection in the real axis.
Use your left arm to represent the complex plane, with your left shoulder representing the origin. For each complex number or operation given to you by your instructor, move your arm so that it points to the appropriate complex number. The prompts are deliberately not given here, as they are best given one-by-one during class. A summary of the prompts appears in the solution.