Express-the-function-f-z-ze-iz-into-cartesian-form-and-separate-it-into-Real-and-Imaginary-part-M-m-

Question Number 180277 by Mastermind last updated on 09/Nov/22

Express the function f (z) = {ze}^{iz} into

cartesian form and separate it into

Real and Imaginary part .

M . m

Commented by Frix last updated on 09/Nov/22

{That}^{'} s what I did before

It seems you {don}^{'} t know much about this \dots

Commented by Mastermind last updated on 09/Nov/22

Smile

okay, lets see in polar form \dots

when z = {re}^{i θ}

Commented by Frix last updated on 09/Nov/22

f (z) = z e^{i z} = r e^{i θ} e^{i r e^{i θ}} =

= r e^{i θ} e^{i r (\cos θ + i \sin θ)} =

= r e^{i θ} e^{- r \sin θ + i r \cos θ} =

= r e^{- r \sin θ + i (θ + r \cos θ)} =

= \frac{r}{e^{r \sin θ}} e^{i (θ + r \cos θ)} =

= \frac{r \cos (θ + r \cos θ)}{e^{r \sin θ}} + i \frac{r \sin (θ + r \cos θ)}{e^{r \sin θ}}

Commented by Mastermind last updated on 09/Nov/22

Thanks man