Express-this-f-z-2z-i-z-i-in-polar-form-where-z-re-i-polar-form-

Question Number 180285 by Mastermind last updated on 09/Nov/22

Express this f (z) = \frac{2 z + i}{z + i} in polar form

where z = {re}^{i θ} (polar form)

Commented by Frix last updated on 09/Nov/22

do some work too

{it}^{'} s similar to the last one, we need the

Cartesian form to get there :

f (z) = \frac{2 r^{2} + 3 r \sin θ + 1}{r^{2} + 2 r \sin θ + 1} - i \frac{r \cos θ}{r^{2} + 2 r \sin θ + 1} =

= \sqrt{\frac{4 r^{2} + 4 r \sin θ + 1}{r^{2} + 2 r \sin θ + 1}} e^{- i \arctan \frac{r \cos θ}{2 r^{2} + 3 r \sin θ + 1}}

Commented by Mastermind last updated on 10/Nov/22

ok

Commented by Mastermind last updated on 10/Nov/22

The thing is kind of complex ooo