Half plane

Cartesian coordinates

The coordinates of the points of the half-plane satisfy the inequality :

Ax + By + C> 0 , where A, B, C are some constants, moreover, A and B are not equal to zero at the same time.

If the straight line Ax + By + С = 0 (the border of a half-plane) is attributed to this half-plane, then such a half-plane is called closed .

Complex coordinates

On the complex plane z = x + iy , the following are considered:

• the upper half-plane y = Im z> 0 ,
• the lower half-plane y = Im z <0 ,
• the left half-plane x = Re z <0 ,
• right half-plane x = Re z> 0 .

• Two points lie on one side of a line if and only if the segment between them does not intersect with this line.
• The half-plane of the complex plane is conformally mapped onto a circle using a linear fractional function . Such a mapping from the upper half-plane to the unit circle (and back) is called the Cayley transformation .

• Semi-straight
• Half space