Polar form of a complex number

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})

\fn_cm r=\sqrt{x^2+y^2}

or
\fn_cm Z=(x,y)=x+iy= r(cos \theta + i sin \theta )
 The plane is known as Argand plane or Argand Diagram or complex plane or Gaussian plane.

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