I am new to phasors/polar numbers. so I am confused as to why when I try to convert $$1-\sqrt{r}*e^{ia} $$ to a polar form on my calculator It comes back with the same thing, indicating this is already in polar form.
The form I want to get it in is $$M*e^{i\phi}$$ (M= magnitude (a real number) , $\phi$ is the phase (also a real number)
I don't understand how this can be if the complex exponential $e^{ia}$ is only multiplied with $\sqrt{r}$ but not $1$.
I intend to multiply this expression with another polar number later and add their phase angles later. I would appreciate any help, and thanks in advance.
No $f=1+ t e^{ia}$ is not in a polar form but we can write it the polar form as $f=R e^{i\theta}$: $$f=1+t\cos a+i t \sin a= R \cos \theta + i R \sin \theta \implies R\cos \theta=1+t\cos a, ~~R\sin \theta= t \sin a $$ $$ \implies R=\sqrt{1+t^2+2t \cos a},~~~ \theta= \tan^{-1}\frac{1+t \cos a}{t\sin a}.$$