Complex plane
In mathematics, the
complex plane or
z-plane is a geometric representation of the complex numbers established by the
real axis and the orthogonal
imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed most easily in polar coordinates – the magnitude or
modulus of the product is the product of the two absolute values, or moduli, and the angle or
argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the
Argand plane because it is used in
Argand diagrams. These are named after Jean-Robert Argand, although they were first described by Norwegian-Danish land surveyor and mathematician Caspar Wessel.