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

Question Number 180159 by Mastermind last updated on 08/Nov/22

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

form and separate it into Real and

Imaginary part .

M . m

Answered by Frix last updated on 08/Nov/22

z \in C

z = a + b i

f (z) = (a + b i) e^{- b + a i} = (a + b i) e^{- b} e^{a i} = \frac{a}{e^{b}} e^{a i} + \frac{b i}{e^{b}} e^{a i} =

= \frac{a}{e^{b}} (\cos a + i \sin a) + \frac{b i}{e^{b}} (\cos a + i \sin a) =

= \frac{a}{e^{b}} (\cos a + i \sin a) + \frac{b}{e^{b}} (- \sin a + i \cos a) =

= \frac{a \cos a - b \sin a}{e^{b}} + \frac{a \sin a + b \cos a}{e^{b}} i

Commented by Mastermind last updated on 09/Nov/22

Thank you man

Commented by Mastermind last updated on 09/Nov/22

But in polar form

Commented by Frix last updated on 09/Nov/22

z e^{i z} is the polar form

and in polar form you cannot seperate the

real and imaginary parts

Facebook Tweet Pin