Let the complex number is a + ib

The polar form of a complex number is represented as

   a + ib = r(cosθ + isinθ)

Where r*cosθ = a .............1

    and r*sinθ = b...............2

Now square both the equations and add them then we get

      r² *cos² θ + r² *sin² θ = a² + b²

=> r² (cos² θ + sin² θ) = a² + b²

 =>r² = a² + b²

 => r = √(a² + b²)

Now divide equation 2 by equation 1, we get

          (r*sinθ)/(r*cosθ) = b/a

=>     tanθ = b/a

=>     θ = tan^-1 (b/a)