• Every complex number can be written in the form \(a + b \, i\).
• Every complex number on the unit circle can be written in the form \(\cos (\theta ) + \sin (\theta ) \, i\).
• Every complex number can be written in the form \(r \cdot (\cos (\theta ) + \sin (\theta ) \, i)\).
• Every complex number can be written in the form \((r, \theta )\).

We are adding two more to the list.

• Every complex number on the unit circle can be written in the form \(e^{i \, \theta }\).
• Every complex number can be written in the form \(r \cdot e^{i \, \theta }\).

Learning Outcomes

In this section, students will

• use the different forms to investigate the Complex Numbers