Math Help Forum - View Single Post - 1 sum. elementary transformation from z-plane to w-plane (complex number)

ssadi · #3 December 3rd, 2008, 07:26 PM

Quote:

Originally Posted by ThePerfectHacker

The path that you take on the circle at origin of radius two can be expressed as $g(\theta) = 2e^{i\theta}$ for $0\leq \theta \leq 2\pi$ .
Under the transformation $z\mapsto z^2$ the path becomes mapped to $\left( 2e^{i\theta} \right)^2 = 4e^{2i\theta}$ for $0\leq \theta \leq 2\pi$ . Because of the presence of $2i\theta$ (rather than $i\theta$ ) it means the points moves twice around a circle of radius 4.

Gotcha, thanks