plz expain argand diagram and its applications??

The complex plane is called an argand diagram. It is used to plot a complex number. On the horizontal axis are the real numbers and on the vertical axis are the imaginary numbers. Here is an example of an argand diagram:

As in polar co-ordinates, a complex number can be defined by its distance from the origin (modulus) and angle (in radians) from the positive real axis (argument). It can be written as (r,θ), wher r is the modulus and θ is the argument. A complex number, x+i.y, is the same as r(cos(θ) + sin(θ)). Then there is an identity r(cos(θ) + sin(θ)) = re^iθ, which can be checked by differentiating both sides. From this comes a very interesting result; e^iπ = -1.