Polar form of a complex number
![](https://www.pakmath.com/wp-content/uploads/2019/02/polar.png)
The polar coordinates of a P are (r,θ) where r is known as modulus and
θ is the argument of a complex number Z.
From above figure
a = r cosθ
b = r sinθ
![\fn_cm a^2+b^2=r^2\\ \,\,\,\,\ \theta= tan^{-1} (\frac{b}{a})](https://latex.codecogs.com/gif.latex?\fn_cm&space;a^2+b^2=r^2\\&space;\,\,\,\,\&space;\theta=&space;tan^{-1}&space;(\frac{b}{a}))
![\fn_cm r=\sqrt{x^2+y^2}](https://latex.codecogs.com/gif.latex?\fn_cm&space;r=\sqrt{x^2+y^2})
or
![\fn_cm Z=(x,y)=x+iy= r(cos \theta + i sin \theta )](https://latex.codecogs.com/gif.latex?\fn_cm&space;Z=(x,y)=x+iy=&space;r(cos&space;\theta&space;+&space;i&space;sin&space;\theta&space;))
The plane is known as Argand plane or Argand Diagram or complex plane or Gaussian plane.