# Argand Plane

*z*=

*a*+

*ib*can be represented as an ordered pain (

*a*,

*b*) and plotted as a point in the X - Y plane.

Some complex numbers are shown as points in the X-Y plane in the diagram below The plane having complex number assigned to each point on it is called a complex plane or Argand plane. In this plane X-axis is called the real axis and Y-axis is called the imaginary axis.

**Note:-**

- All complex numbers which are purely real on X-axis.
- All complex numbers which are purely imaginary on Y-axis.
- The origin corresponds to 0 + 0i

^{ }is the conjugate of P(x, y) As you can see in the diagram,

^{}is the mirror image of P on real axis.

b) How to represent negative of a complex number in the Argand Plane.

P(x, y) has its negative p^{1}(-x, -y). If P is in the first Quadrant, P

^{1}is in the third quadrant. If another complex number Q is in the second quadrant, its negative is in the fourth quadrant. In general, the negative of aomplex number in the Argand plane is a reflection about the origin or a rotated image of the original number through 180Â°.