1.3 Complex or Argand Plane

A complex number $z = x + iy$ is exclusively determined by an ordered pair of real number $(x,y)$. The numbers $2 - 5i$, 8 and $- 7i$ are equivalent to $(2, - 5)$, $(8,0)$ and $(0, - 7)$ respectively. In this manner, a complex number $z = x + iy$ can be represented by the point $(x,y)$ in the coordinate plane.

If we consider $x$ - axis as real axis and $y$ - axis as imaginary axis to represent a complex number, then the $xy$ - plane is called complex plane or Argand plane. It is named in honour of the Swiss mathematician Jean Argand (1768- 1822).

A complex number is represented not only by a point, but also by a position vector pointing from the origin to the point. The complex number, the corresponding point and the vector are all typically denoted by the same symbol, $z$. Geometrically, a complex number can be interpreted either as a point in the complex plane $C$ or as a vector in the Argand plane.