We have many descriptions of our 2D Complex Number System:

• Points with Rectangular Coordinates, \((a,b)\)
• Vectors with Rectangular Coordinates, \(\langle a, b \rangle \)
• Points with Circular Coordinates, \((r,\theta )\)
• Numbers with Rectangular Dimensions, \(a + b \, i\)
• Numbers with Angles and Radii, \(r \, (\cos (\theta ) + i \, \sin (\theta ))\)
• Numbers via Exponentials, \(e^{r + i \, \theta }\)

These are all describing the same structure, which means all of these descriptions must be mathematically connected.

The bridges connecting all of these are built from Trigonometry, Hyperbolic-Trigonometry, and Exponential Algebra.

Learning Outcomes

In this section, students will

• explore the arithmetic of Complex Numbers.