# How to convert this complex number to exponential form? [closed]

I have $$Z = {\frac{2+i}{2-i}}$$. I need to write it in exponential form, i.e. $$Z = r*e^{i{\phi}}$$.

I simplified the given example to $${\frac{3 + 4i}{5}}$$, i.e. $$a={\frac{3}{5}}, b={\frac{4}{5}}$$. Therefore, $$r = 1$$.

Then I calculate $$cos({\phi}) = a / r = 3 / 5, sin({\phi})=b/r = 4/5$$. How do I calculate $${\phi}$$ from here?

The online Complex Number Exponential Form given $${\phi}=tan^{-1}({\frac{4}{3}})$$.

{Abs, Arg}@((2 + I)/(2 - I)) // Through