the cartesian plane is divided into four regions or octants.
the cartesian plane is divided into four regions or?
octants
a euclidean plane with a chosen cartesian coordinate system is called a "cartesian plane". in a cartesian plane one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at and ), the unit hyperbola, and so on.





























the two axes divide the plane into four right angles, called "quadrants". the quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the "first quadrant".
cartesian coordinate system
upper half-plane





























in mathematics, the upper half-plane is the set of points in the cartesian plane with  0.





























section::::complex plane.





























mathematicians sometimes identify the cartesian plane with the complex plane, and then the upper half-plane corresponds to the set of complex numbers with positive imaginary part:





























the term arises from a common visualization of the complex number as the point in the plane endowed with cartesian coordinates. when the y-axis is oriented vertically, the "upper half-plane" corresponds to the region above the x-axis and thus complex numbers for which "y"  0.
upper half-plane