Illustration of the mapping of the complex plane by the complex cosine function, w = cos(z). Left:The z-plane with the four complex numbers 0, 1, i and 1 + i, a quadratic net with mesh size 0.5, part of the vertical stripe –π &lt; Re(z) &lt; π (marked with a light gray background) as well as two rectangles colored green and cyan. Right: The cosine images of these objects: Horizontal lines are mapped onto ellipses, vertical ones onto hyperbolas, all of which have focal points at –1 and 1. They form curves which locally intersect each other perpendicularly.
Own work
AstroOgier