State Plane Coordinate System State Plane Coordinate System The State Plane Coordinate System (SPS or SPCS) is a set of 124 geographic zones or coordinate systems designed for specific regions of the United States. Each state contains one or more state plane zones, the boundaries of which usually follow county lines. There are 110 zones in the contiguous US, with 10 more in Alaska, 5 in Hawaii, and one for Puerto Rico and US Virgin Islands. The system is widely used for geographic data by state and local governments. Its popularity is due to at least two factors. First, it uses a simple Cartesian
Complex plane notation the complex number "z" corresponds to the point ("x", "y") in the Cartesian plane. In the Cartesian plane the point ("x", "y") can also be represented in polar coordinates as In the Cartesian plane it may be assumed that the arctangent takes values from −"π/2" to "π/2" (in radians), and some care must be taken to define the "real" arctangent function for points ("x", "y") when "x" ≤ 0. In the complex plane these polar coordinates take the form where Here |"z"| is the "absolute value" or "modulus" of the complex number "z"; "θ", the "argument" of "z", is