Trigonometric form and exponential polar form

Using the polar coordinates $(\rho,\theta)$ of the point representing $z$ one obtains the trigonometric form $z=\rho(\cos\theta+i\sin\theta)$ and, through Euler’s identity, the exponential form $z=\rho\,e^{i\theta}$. In these forms the product, quotient and power become very simple (De Moivre’s formula) and multiplication acquires a geometric meaning of rotation and dilation. The section closes with the parametrisation of curves in the plane.

• Trigonometric form and argument
• Euler’s identity and exponential form
• Product and power in exponential form
• Parametrisation of curves in the plane
• Implicit form and parametric form